IN  MEMORIAM 
FLORIAN  CAJOR1 


THE  PRIMARY 
PUBLIC  SCHOOL  ARITHMETIC 


THE  PRIMARY 
PUBLIC  SCHOOL  ARITHMETIC 


BASED    ON 
McLELLAN  AND  DEWEY'S  "PSYCHOLOGY  OF  NUMBER" 


BY 
J.  A.  McLELLAN,  A.M.,  LL.D. 

PRESIDENT  ONTARIO  NORMAL  COLLEGE 
AUTHOR  (WITH  DR.  DEWEY)  OF  "TUB  PSYCHOLOGY  OF  NUMBER,"  "APPLIED 

PSYCHOLOGY,"    "ELEMENTS  OF  ALGEBRA,"   ETC. 
AND 

A.  F.  AMES,  A.B. 

HONOR  GRADUATE   IN  MATHEMATICS  J    FORMERLY  MATHEMATICAL 

MASTER,   ST.   THOMAS  COLLEGIATE  INSTITUTE 
SUPERINTENDENT  OF  SCHOOLS,   RIVERSIDE,   ILL.     " 


TEACHERS'  EDITION 


Nefo  god* 
THE    MACMILLAN   COMPANY 

LONDON :  MACMILLAN  &  CO.,  LTD. 
1899 

All  rights  reserved 


COPYBIOHT,  1898, 
BY  THE  MACMILLAN  COMPANY. 


Set  up  and  electrotyped  May,  1898.      Reprinted  August, 
1898 ;  December,  1899. 


Norfoooti 

J.  8.  Gushing  &  Co.  -  Berwick  &  Smith 
Norwood  Masi.  U.S.A. 


/v 


O 


PKEFACE 


THIS  book  is  strictly  introductory  to  "The  Public 
School  Arithmetic,"  and  forms  with  it  a  complete  course. 
In  both,  the  method  of  treatment  closely  follows  "  The 
Psychology  of  Number."  A  few  special  points  in  the 
Primary  may  be  noticed. 

1.  While  number  work  in  the  first  grade  may  be 
largely  incidental,  it  ought  not  to  be  accidental.  The 
teacher  should  have  a  clear  conception  of  the  work  to  be 
done,  and  of  the  order  and  method  by  which  the  child 
may  step  by  step  reach  the  desired  end.  When  the  child 
enters  school  the  number  sense  is  alert;  he  is,  roughly 
speaking,  in  the  counting  stage  of  development.  Upon 
the  principle  "  strike  while  the  iron  is  hot,"  this  counting 
power  should  at  once  be  used  for  further  growth  by 
applying  it  to  more  definite  measurements.  Such  appli- 
cation arouses  fresh  interest  in  number,  and  is  in  a  high 
degree  educative.  On  this  point  Dr.  Dewey  says,  "Unless 
there  is  to  be  arrested  development  when  the  child  enters 
school,  some  function  must  be  found  with  reference,  to 
which  he  may  utilize  his  ability  to  count  —  the  number 
sense  becomes  vitalized  and  truly  educative  at  this  point  by 
being  largely  directed  towards  the  definition  of  values  in  the 
form  of  measurement"  This  book,  therefore,  while  not 

y 


yi  PREFACE 

giving  first  grade  work  in  full,  presents  in  systematic 
form  and  in  sufficient  detail  for  any  primary  teacher  the 
amount  of  work  to  be  done  and  the  method  of  doing  it. 

2.  Those  to  whom  counting  is  the  whole  of  number 
hold  that   almost   the   sole   object   of    number-work   in 
primary  grades  is  quickness  and  accuracy  in  the  figure- 
work  of  the  fundamental  rules.     They  are  inclined  to 
belittle  the  training  of  intelligence.     Most  teachers  know, 
however,  that  not  accurate  figure-work  and  rule-learning 
is  the  crux,  but  rather  what  figure-work  —  "  what  rule  " 

—  to  apply  in  given  cases.  Accordingly,  while  not  un- 
mindful of  the  use  of  skill  in  figure-work,  the  authors  of 
this  book  have  a  wider  purpose.  Recognizing  that  num- 
ber is  the  "  tool  of  measurement,"  they  have  endeavored  by 
a  careful  grading  and  an  unusual  variety  of  concrete  and 
constructive  exercises  to  develop  true  ideas  of  number 
and  numerical  operations,  as  well  as  trained  intelligence 
and  ability  to  apply  what  has  been  learned  to  the  varying 
problems  of  social  life. 

3.  There  are  two  extreme  views  regarding  the  nature 
of  number  leading  to   two  quite   different   pedagogical 
methods:  one  of  these,  No  ratio  in  number;  the  other, 
No  number  in  ratio.     The  one  begins  with  the  ratio  idea, 
and  ignores  or  subordinates  the  "  how  many  "  (counting) 
idea,  letting  it  struggle  into  being  incidentally  in  the 
development  of  ratio.     The  other  begins  with  the  vague 
"how  many,"  and  subordinates  ratio  or  rather  totally 
ignores  it  as  not  involved  in  the  number  process.     This 
book,  following  as  it  does  "  The  Psychology  of  Number," 
avoids  both  extremes.      It  begins  with  the  how  many 
(counting)  as  applied  to  some  total ;  and  keeping  together 


PREFACE  vii 

things  which  psychologically  cannot  be  separated,  viz. 
number  and  quantity,  proceeds  from  the  vague  how  many 
and  the  vague  how  much  to  the  definite  so  many  and  the 
definite  so  much.  Thus  there  is  gradually  yet  surely 
evolved  the  concept  of  ratio  —  a  concept  which  is  indis- 
pensable in  practical  life,  and  without  which  there  can 
be  no  Science  of  Arithmetic.  On  this  important  point 
Dr.  Dewey —  whose  views  on  the  psychical  nature  of 
number  have  never  been  questioned  by  a  competent 
critic  —  says :  "  When  counting  is  used  by  the  child  to 
value  some  amount  or  other  the  ratio  idea  is  implied.  It 
need  not,  therefore,  be  consciously  or  explicitly  stated. 
In  fact,  I  should  say  that  for  a  considerable  period  it 
should  not  be.  It  is  enough  that  the  child  gets  a  sense 
for  the  use  and  application  of  number  in  measurement. 
When  number  is  so  used,  the  transition  to  the  conscious 
ratio  idea,  whether  in  the  form  of  ratio  proper,  or  frac- 
tions, or  percentage,  is  natural  and  inevitable ;  this  is  not 
a  mere  doctrinaire  statement ;  it  rests  upon  continuous 
experimenting  and  observation  in  a  school  where  the 
child's  number  sense  is  developed  in  connection  with 
constructive  operations  in  manual  training,  in  which 
number  relations  are  introduced  as  instruments  to  prac- 
tical valuation." 

4.  This  has  been  verified  during  the  preparation  of 
this  book.  Through  the  kindness  of  the  publishers 
printed  sheets  of  the  exercises  and  methods  have  been 
placed  in  the  hands  of  teachers  in  training  (and  public) 
schools,  and  actually  tested  in  the  classes.  The  reports 
have  been  unanimously  favorable.  The  children  got  hold 
of  the  idea  of  number  as  "  The  Tool  of  measurement," 


yiii  PREFACE 

as  playing  an  important  part  in  the  affairs  of  life ;  school 
life  was,  in  one  respect  at  least,  seen  to  be  a  part  of  social 
life.  It  followed  that  interest,  enthusiasm,  self-activity 
in  connection  with  arithmetical  work  became  the  com- 
mon experience  in  the  schools. 

For  help  in  such  experimenting  our  thanks  are  due  to 
a  number  of  successful  teachers,  especially  to  Principal 
Graham  of  the  London  Training  School,  to  Principal 
Elliott  of  the  Hamilton  Training  School,  to  Mrs.  Ran- 
dolph (Los  Angeles),  and  to  Principal  William  Sparks 
of  Chatham. 

Teachers  are  recommended  to  study  with  care  Dewey 
and  McLellan's  "  Psychology  of  Number,"  and  the  "  Pub- 
lic School  Arithmetic,"  which  illustrates  so  many  points 
in  the  "  Psychology  of  Number." 

The  "Teachers'  Edition"  of  this  book  will  contain  all 
needed  answers  to  problems,  suggestions  for  first  grade 
work,  some  illustrative  lessons,  and  many  suggestions  as 
to  methods. 


CONTENTS 


PAOB 

SUGGESTIONS  TO  TEACHERS     .        .        .        .  .  xi 

SUGGESTIVE  LESSONS xxviii 

SUGGESTIONS Ixiv 

SECTION  I 
FIRST  GRADE  WORK  REVIEWED 1 


SECTION  II 

FUNDAMENTAL  ADDITIONS  EXTENDED  —  SUBTRACTION  —  DE- 
NOMINATE NUMBERS  —  QUANTITY  —  UNIT  OF  MEASURE  — 
NUMBER 20 

SECTION  III 

MULTIPLICATION  TABLES  OF  2  AND  3  —  DIVISION  —  DENOM- 
INATE NUMBERS  —  SQUARES  AND  OBLONGS  —  FRACTIONS 

—  RATIO 63 

SECTION  IV 

MULTIPLICATION  TABLES  OF  4  AND  5  —  DIVISION  —  DENOM- 
INATE NUMBERS  —  SQUARES  AND  OBLONGS  —  FRACTIONS 

—  RATIO 98 

SECTION  V 

FUNDAMENTAL  ADDITIONS  EXTENDED  —  SUBTRACTION  —  MUL- 
TIPLICATION TABLES  OF  5  AND  6  —  DIVISION  ,  ,  J21 

is 


X  CONTENTS 

SECTION   VI 

PAGE 

DOLLARS  AND  CENTS  —  MISCELLANEOUS  REVIEW  QUESTIONS     137 

SECTION   VII 
ADDITION  —  SUBTRACTION  —  MULTIPLICATION  —  DIVISION  — 

RATIO  —  DENOMINATE  NUMBERS  —  VOLUME    .        .         .     148 

SECTION  VIII 
ROMAN  NOTATION  —  FRACTIONS 163 

SECTION  IX 

TABLE  OP  DENOMINATE  NUMBERS  —  FUNDAMENTAL  OPERA- 
TIONS —  MULTIPLICATION  TABLE  .....  178 

SECTION  X 

NUMERATION  AND  NOTATION  —  ADDITION  TABLE  —  MULTI- 
PLICATION WITH  Two  FIGURES  IN  THE  MULTIPLIER  — 
LONG  DIVISION  . 194 

SECTION  XI 
DECIMALS 210 

SECTION  XII 
PERCENTAGE 224 

SECTION  XIII 
MISCELLANEOUS  REVIEW  LESSONS  240 


ANSWERS         ,        ,        ,        ,        «        t        t        f        ,         ,     255 


SUGGESTIONS  TO   TEACHERS 


Pages  xi  to  xxvii  of  Suggestions  to  Teachers  indicate 
the  kind  of  work  that  should  be  done  by  the  class 
previous  to  beginning  Lesson  1  of  this  book.  Les- 
sons 1  to  8  review  the  work  of  this  section. 

I.  Counting.  —  Counting  is  of  course  the  first  thing 
to  look  after :  the  child  can  probably  count  a  little 
when  he  enters  school,  but  there  is  now  to  be  count- 
ing with  a  definite  end  in  view  —  the  growth  of  the 
relating  process  which  gives  rise  to  number ;  there 
is  a  whole  to  get  an  idea  of,  —  there  are  its  parts ; 
there  is  the  how -many ;  i.e.  the  child  is  counting 
something. 

1.  (a)  Start  with  a  whole  and  count  by  single 
things.  For  instance,  count  the  number  of  girls  in 
the  room.  Of  boys.  Of  children.  Test  how  far  the 
number  names  are  significant ;  e.g.  name  the  num- 
ber and  have  corresponding  objects  selected,  etc. 

(6)  It  may  be  that  the  children  cannot  count  — 
cannot  give  the  consecutive  number  names  and  apply 
them  to  corresponding  groups  of  objects.  In  this  case 
the  starting-point  is  the  vague  muchness  (ideas  of 
more  and  less)  and  the  vague  how-many  which  must 

xi 


xii  SUGGESTIONS   TO   TEACHERS 

be  in  the  children's  minds.  Have  them  make  com- 
parisons involving  ideas  of  more  and  less ;  e.g.  the 
length  of  the  desk  is  greater  than  the  width,  etc. 
Also  practice  in  the  how-many  idea ;  e.g.  compare 
the  how-many  cubes  (say  8)  in  this  group  with  the 
how-many  (say  6)  in  that.  They  will  be  led  to  see 
that  the  muchness  of  a  quantity  is  determined  by  the 
how-many  parts  in  it,  etc.  Have  constructive  exer- 
cises, bringing  out  relations  of  consecutively  num- 
bered objects  (how  five  differs  from  six,  etc.),  and 
arousing  interest  in  number  names ;  e.g.  have  them 
make  a  picket  (two  splints) ;  try  to  make  a  triangle 
with  two  splints  ;  they  will  need  one  splint  more,  and 
will  express  the  how-many  as  "  two  and  one,"  or  as 
"one,  and  one,  and  one"  Similarly,  try  to  make  a 
square  with  three  splints ;  they  will  need  one  more 
splint,  and  the  how-many  in  the  square  will  perhaps 
be  expressed  as  "  three  and  one,"  or  "  two  and  one 
and  one,"  or  (as  we  have  often  seen)  "  one  and  one' 
and  one'  and  one,"  with  some  rhythmic  movement. 
They  will  now  fully  appreciate  the  simple  number 
names  which  are  substitutes  for  the  round-about  ex- 
pressions. 

The  children  will  hence  soon  be  ready  to  see  that 
we  cannot  find  how  much  one  quantity  (as  a  line, 
area,  etc.)  differs  from  another  without  finding  the 
how-many  of  some  one  thing  (unit)  in  each. 

2.  Not  to  be  confined  to  single  things.  —  Count  this 
IWQ  rows  of  girls;  of  boys ;  of  all,  —  how  many 


SUGGESTIONS  TO  TEACHERS  xiii 

twos?  Count  pairs  of  hands,  —  how  many  pairs? 
Similarly,  count  groups  of  3,  —  how  many  threes, 
etc.  ?  Also  appeal  to  the  ear :  taps  with  stick, 
strokes  of  bell,  vocal  sounds  (as  letters,  etc.),  this 
both  with  single  sounds,  and  groups  of  sounds  (i.e. 
sounds  rhythmically  marked  off). 

3.  Test  this  relating  process,  e.g.  start  counting 
with  4,  i.e.  4,  5,  6  (units  of  any  kind).     Show  by 
fingers  or  marks  or  dots  what  preceded  the  4. 

4.  Count  the  same  quantity  with  different  units 
or  groups,  e.g.  these  12  pupils  :  by  2's,  how  many? 
(6).     By  3's,  by  4's,  by  6's,  how  many  in  each  case  ? 
This  lot  of  24,  by  2's,  by  3's,  by  4's,  etc.,  to  deter- 
mine the  different  numbers  (how  many)  that  measure 
the  same  quantity.     Also  count  different  quantities 
with  the  same  unit  of  measure.    This  lot  of  6  (pupils, 
etc.)  by  3's.     This  group  of  12  by  3's,  this  group  of 
15  by  3's,  etc.     Use  many  familiar  units. 

5.  Represent  the  various  units  by  dots   on   the 
blackboard;  e.g.  these  rows  of  dots  represent  groups 
of  two  (pupils,  cents,  etc.)  each,  J  J  how  many  ? 

•  •  •  •  • 

(4).  This  group  of  three  each,  •  •  •  •  •  how 
many  ?  How  many  4's  ?  etc. 

6.  Let  all  the  foregoing  be  then  extended  to  exact 
measurements.     Count  the  2-inches  in  this  foot-rule 
(or  line);  the  3-inches,  etc.     Count  the  number  of 
3-inches  in  lines  12  in.,  15  in.,  18  in.,  etc.,  long,  and 
so  on. 


xiv        SUGGESTIONS  TO  TEACHERS 

7.  Cut  out  of  cardboard  strips,  respectively,  1  in., 
2  in.,   3  in.,  ...  12  in.  long.     Ask  the  pupils  to 
select  the  3  in.  strip,  the  5  in.  strip,  etc. 

8.  Have  bags  of  sand  or  other  material  weighing 
from  1  to  10  Ib.     Let  the  pupils  lift  these  and  guess 
their  weights. 

9.  Make  squares  whose  sides  are  respectively  2, 
3,  and  4  in.     Cut  them  into  parts  each  containing 
1    sq.    in.      Count   the    parts   and    then    put    them 
together  again  to  form  the  original  square.     Count 
the  2-sq.  in.,  etc. 

10.  Similarly,  make  oblongs  2  in.  by  3  in.,  or  3  in. 
by  4  in.,  for  example;   divide  into  inch  squares  or 
half-inch  squares,  count,  and  again  reconstruct  the 
whole  from  the  parts.    Count  as  in  9  the  2-sq.  in.,  etc. 

11.  Make  simple  measurements  with  the  foot-rule 
and  tape  measure ;  for  instance,  measure  the  width 
of  the  desk,  the  length  of  the  table,  the  height  of  the 
children,  the  number  of  inches  around  the  head,  the 
distance  around  the  chest  when  expanded  or  con- 
tracted. 

12.  Take  two  points,  say  2  or  3  or  4,  etc.,  yards 
apart,   without  the   pupils   knowing  what   distance 
was  measured.     Let  the  pupils  measure  the  distance 
between  the  points  with  a  yardstick.     What  num- 
ber do  you  get  ?     How  many  yards  ?     Measure  with 
a  foot-rule.     How  many  feet  ?     Measure  with  a  unit 
one-half  foot  long.    What  number  do  you  get  ?    How 
many  half-feet  ?     Write,  2  yd.  =  6  ft.  =  12  half -feet. 


SUGGESTIONS  TO  TEACHERS  XV 

Put  (say)  2,  3,  4,  etc.,  quarts  of  water  into  a  pail. 
Let  the  pupils  measure  it  out  with  a  quart  measure. 
What  number  do  you  get  from  the  measurement? 
With  a  pint  measure  what  number  do  you  get  ? 
With  a  gill  measure  what  number  do  you  get? 
Write,  2  qt.=4  pt.  =  16  gi. 

13.  Draw  a  line  12  in.  long,  without  the  pupils 
knowing  its  length.  Measure  it  with  an  inch  unit. 
What  number  do  you  get?  How  many  inches? 
Measured  with  a  2-inch  unit  what  number  ?  How 
many  2-inches  ?  With  a  3-inch  unit  what  number  ? 
How  many  3-inches  ?  So  also  with  4-inch  and  6- 
inch  units.  Draw  and  measure  other  lengths  with 
other  units. 

II.  Instantaneous  recognition  of  the  number  pict- 
ures. —  The  work  suggested  in  the  above  outline 
should  lead  as  directly  as  possible  to  the  instanta- 
neous recognition  of  the  number  pictures  —  which 
will  aid  in  complete  mastery,  especially  for  the  aggre- 
gation idea  of  addition  and  subtraction,  of  the  num- 
bers from  1—10. 

The  picturing  power  should  be  used,  in  fact  must 
be  used,  for  economy  of  energy.  If  this  picturing  is 
rightly  used,  the  whole  analysis  of  ten  will  be  given 
(perceived  at  last)  in  the  picture  *•*  I  *•*  no  matter 
what  units  are  represented. 

It  must  be  understood  that  the  symbolizing  dots 
stand  for  any  units  whatever ;  e.g.  *•*  stands  for 


XVI  SUGGESTIONS  TO  TEACHERS 

not  only  5  single  cents,  but  five  2-ct.,  five  3-ct.,  five 
5-ct.,  five  dollars,  five  2  boys,  five  3  apples,  etc.,  etc. 

1.  Let  the  children  count  a  number  of  beans,  say 
eight,  and  separate  them  into  two  equal  parts.    How 
many  parts  are  there  ?     Separate  each  part  into  two 
equal  parts.     How  many  of  these  parts  are  there 
in  each  part?     How  many  beans  are  there  in  each 
part  ?     Or,  arranging  in  perceptive  forms,  how  many 
ones  in  *  ?     How  many  twos  in  J    *  ?     How  many 
pairs  of  twos  in  J    |  *  *  ?      Similar  exercises  and 
questions  may  be  given  with   splints   formed   into 
two  squares,  and  into  two  groups  of  two  pickets 
each.     Treat  an  oblong  4  in.  by  2  in.  similarly. 

2.  Put  1-in.  units  together  to  form  the  2-in.  unit, 
2-in.  units  to  form  the  4-in.  unit,  4-in.  units  to  form 
the  8-in.  unit,  and  so  on.     Use  also  sq.  in.  units. 


3.  In  the  above  arrangement  of  dots  there  are 
how  many  single  units  ?  How  many  2-units  or  twos  ? 
How  many  3-units  or  threes?  Use  this  arrangement 
to  fix  the  place  of  5  in  the  sequence  between  4  and  6, 
i.e.  as  1  more  than  4  and  1  less  than  6.  Make  with 
sq.  in.  a  square,  side  2  in.,  and  an  oblong  2  in.  by  3 
in.  Give  the  pupils  5  sq.  in.  to  work  with. 


4.  Similarly,  use  this  arrangement   to   show   the 


SUGGESTIONS  TO  TEACHERS  xvii 

relation  of  8  to  4,  as  two  fours,  and  to  fix  the  place 
of  7  in  the  sequence  between  6  and  8,  i.e.  as  1  more 
than  6  and  1  less  than  8. 


5.  Similarly,  show  the  relation  of  10  to  5,  and  fix 
the  position  of  9  in  the  sequence  between  8  and  10, 
i.e.  as  1  more  than  8  and  1  less  than  10. 

6.  In  using  these  dot  arrangements,  the  picturing 
power  should  be  definitely  cultivated.      Five  dots 
should  be  instantly  recognized  as  5,  6  as  6,  7  as  5 
and  2  or  4  and  3,  8  as  two  4's  or  four  2's,  9  as  5  and 
4,  10  as  two  5's  or  five  2's,  and  also  other  simple 
relations  within  the  groups. 

7.  After  making  the  analysis  of  the  visual  forms, 
for  instance,  5  +  1  =  6,  4  +  2  =  6,  etc.,  cover  the  5 
dots.    How  many  are  hidden  ?    How  many  are  seen  ? 
Cover  the  4.     How  many  are  hidden  ?     How  many 
seen  ?     So  on,  taking  care  that  6  is  seen  as  5  +  1  and 

1  +  5,  4  +  2  and  2  +  4,  and  so  on. 

8.  In   every  case   practical   examples    should   be 
used  as  much  as  possible  ;   e.g.  in  the  five.     Cover 

2  dots.     What  do  you  see?  (3).     How  many  are 
unseen?  (2).     Then  what  must  be  done  with  the 

3  to  get  5  ?     With  3  f  to  get  5  ^  ?     With  3  eggs  to 
make  up  6    eggs  ?     With  3  dollars  to  make  up  7 
dollars?      With   3   dimes   to    make    up    8    dimes? 
With  3  2-dollar  bills  to  make  5  2-dollar  bills  ?  etc. 
Count  8  by  2's  :  how  many  ?     With  8  f  how  many 


xviii  SUGGESTIONS  TO  TEACHERS 

apples  2^  each  can  be  bought?  etc.  Connecting 
thus  the  practical  work  with  the  child's  own  experiences 
as  closely  as  possible.  With  8  ten-dollar  bills  bought 
cows  at  2  ten-dollar  bills  each.  How  many?  All  the 
combinations  up  to  ten  (including  some  of  the  factor 
relations)  can  be  mastered  in  a  few  weeks.  The 
practical  element  will  make  the  work  deeply  interest- 
ing to  the  child. 

9.    Arrange  on  separate  pieces  of  cardboard  dots 
placed  thus  : 


Show  these  cards  separately  to  the  class  and  have 
the  answer  given  instantly.  Tell  how  many  two's 
in  6  ?  in  8  ?  in  10  ?  Show  the  10  picture  an  instant; 
unseen,  erase  one  dot,  show  for  an  instant  what  is 
left.  What  number  ?  What  was  done  with  the  10  ? 
Thus  also  erase  two  dots,  etc.  Similarly,  change  6 
to  8,  7,  9,  etc.  Make  practical  examples  as  in  §  8. 

10.  Cut  out  of  cardboards  units  1  in.,  2  in.,  3  in., 
...  10  in.  long,  respectively.  Let  the  children 
select  the  units  which  are  together  equal  to  the  3-in. 
unit ;  to  the  4-in.  unit ;  to  the  5-in.  unit.  Select 
the  units  which  will  make  triangles  each  of  Avhose 
sides  is  respectively  6  and  7  in.  long.  Select  the 


SUGGESTIONS  TO  TEACHERS  xix 

units  which  will  make  squares  whose  sides  are  respec- 
tively 8  and  9  in.  long.  Select  the  units  which  will 
make  a  five-sided  figure,  each  of  whose  sides  is  10 
in.  long. 

11.  Simple  work  from   dictation,  —  for   instance, 
make  a  square  each  side  of  which  is  4  in.      Out  of 
each  corner   cut   1    sq.   in.      Fold,   making  a  box. 
Give  similar  constructive  work. 

12.  Count  by  2's   the   number  of  hands   of   the 
children  in  the  first  row ;  of  the  girls ;  of  the  boys ; 
of  all  the  children  in  the  class.     Count  thus  :  2,  4, 
6,  8,  10,  etc. 

13.  Give    exercises    by    dot    arrangements    and 
measurements  leading  to   and   developing  the  idea 
that  for  any  given  quantity  any  one  measurement 
gives  a  second  measurement. 

Thus  *  *  signifies  that  the  unit  2  measures  6 
three  times,  and  also  that  the  unit  3  measures  6 
twice.  12  by  3's  implies  12  by  4's.  15  by  3's  im- 
plies 15  by  5's,  and  so  on.  Illustrate  by  dots.  12  in. 
by  3  in.  implies  12  in.  by  4  in.  Practical  examples. 

14.  Cut  a  measure  1  ft.  long  out  of .  cardboard. 
Cut  this  foot  measure  into  parts  each  6  in.  long. 
How  many  parts  are  there  ?     Place  two  6-in.  meas- 
ures  end   to   end.       How  long  are  they  together? 
Cut  a  foot  measure  into  parts  each  2  in.  long.     How 
many  parts  are  there  ?     Place  six  2-in.  measures  end 
to  end.     How  long  are  they  ? 

15.  Arrange  constructive  exercises  similar  to  those 


XX  SUGGESTIONS  TO  TEACHERS 

in  paragraph  14,  dividing  1  ft.  into  4-in.  and  3-in. 
units,  respectively.  Make  also  equilateral  triangles 
and  squares  and  note  the  number  in  each  case. 

16.  Cut  out  of  cardboard  units  of  measure  respec- 
tively 6  in.,  4  in.,  3  in.,  and  2  in.  long.     Find  the 
number  of  times  that  each  unit  measures  1  ft. 

17.  Divide   1  ft.  into  2,  3,  4,  and  6  equal  parts, 
respectively.     How  long  are  the  equal  parts? 

18.  Apply  the  foot  measure  to  measure  the  yard. 
What  number  do  you  get  ?    How  many  ft.  ?    3  ft.  in 
what  ?    Apply  the  yard  to  measure  the  length  of  the 
room  and  other  quantities.     How  many  yd.  ?  6  yd. 
in  what  ?     Apply  the  pint  to  measure  the  quart,  the 
quart  to  measure  the  gallon,  and  the  pint  to  measure 
the  gallon.     What  numbers  do  you  get  ?    How  many 
pt.  ?    How  many  qt.?    4  qt.  in  what  ?    8  pt.  in  what  ? 

19.  Count  off  12  objects  into  unit  groups  of  4 
each.     What  is  the  number  of  groups?     Similarly, 
count  off  15  objects,  18  objects,  etc.,  into  groups  of 
5,  6,  etc.,  and  count  the  number  of  groups. 

20.  Have   each    child   form    out   of   splints   two 
squares  with  their  diagonals,  thus:  EJ.     Arrange  each 
square  into  triangles.     How  many  squares  are  there  ? 
How  many  triangles  ?    How  many  pairs  of  triangles  ? 

21.  Measure  a  12-in.  length  with  a  6-in.  unit,  and 
then  again  with  a  3-in.  unit.     How  many  6-in.  units 
in  the  whole?     How  many  3-in.  units  in  the  6-in. 
unit  ?     How  many  3-in.  units  in  the  whole  ?     Simi- 
larly, a  16-in.  length  with  8-in.,  4-in.,  2-in.  units,  etc. 


SUGGESTIONS   TO   TEACHERS  XXI 

III.  Combination  of  the  ten  units.  — 1.  While  the 
pupils  were  studying  the  number  pictures  in  II  they 
were  given  many  practical  questions  on  the  com- 
binations of  single  units.  While  they  study  the 
work  outlined  in  III,  give  them  many  similar  prac- 
tical questions  on  the  combinations  of  the  10-unit, 
in  fact,  on  all  the  combinations  that  have  been 
studied  in  the  number  pictures.  Thus : 

(1)  I  sold  3  cows  for  6  ten-dollar  bills.     How 
much  for  each  ?     How  many  dollars  ? 

(2)  A  tailor  sold  4  suits  of  clothes,  receiving  2 
ten-dollar  bills  for  each.     How  much  did  he  get  for 
all  ?     How  many  dollars  ? 

(3)  I  gave  $  80  for  a  horse ;  how  many  ten-dollar 
bills  will  pay  for  it  ? 

(4)  I  bought  a  suit  of  clothes  for  $  40  and  an 
overcoat  for  $30.     What  did  both  cost  ?     How  many 
ten-dollar  bills  would  pay  for  both  ? 

(5)  I  bought  a  horse  for  $  300  and  2  cows  at  $  40 
each.     What  did  all  cost  ? 

(6)  I  gave  4  dimes  for  a  necktie  and  one-half  as 
many  for  a  collar.     What  did  both  cost  ? 

(7)  Write  in  figures  :  six,  twenty-five,  forty-four, 
eighty,  one  hundred  and  thirty-six,  seven  hundred 
and  seventy-two,  two  hundred  and  four. 

2.  Teach  combinations  of  the  ten  units  in  the  fol- 
lowing manner :  Take  a  cubic  centimeter  (if  a  cubic 
centimeter  cannot  be  procured,  take  a  half-inch  or  an 
inch  cube)  for  the  primary  unit  of  measure ;  a  rec- 


xxii  SUGGESTIONS  TO  TEACHERS 

tangular  prism  (a  decimeter  in  length),  equal  to  ten 
of  these  units,  will  be  the  10-unit  and  ten  of  these 
the  100-unit.  The  units  may  be  of  different  colors 
and  the  units  of  the  decimeter  alternately  white  and 
black.  Let  the  notation  accompany  thus,  —  one  ten 
and  no  units  equals  10,  two  tens  and  no  units  equals 
20,  and  so  on  up  to  ten  tens  which  equals  the  new 
unit  one  hundred,  i.e.  100.  Thus  a  rectangular 
prism,  whose  surface  is  a  square  decimeter  and 
thickness  one  centimeter,  will  be  equal  to  ten  of 
the  10-unit  and  will  be  the  100-unit.  Ten  of  these 
units  will  be  the  1000-unit.  Let  the  notation,  as 
before,  accompany  the  recognition  of  the  facts. 

In  case  the  cubes  referred  to  above  cannot  con- 
veniently be  obtained,  units,  tens,  and  hundreds  can 
be  cut  out  of  cardboard,  the  square  centimeter  (about 
f  in.  on  each  side)  instead  of  the  cubic,  a  strip  1 
decimeter  long  and  1  centimeter  wide  for  the  10-unit, 
and  a  square  decimeter,  divided  into  ten  strips, 
colored  alternately  white  and  black,  for  the  100- 
unit.  Extend  this  as  suggested  in  paragraphs  8 
and  9. 

3.  Give  the  pupils  the  number  names  from  one  to 
thirteen  inclusive.  Explain  13  as  3  and  10,  teen 
being  ten.  Ask  them  to  suggest  a  name  for  14,  i.e. 
4  and  10,  which  is  fourteen,  and  so  on  up  to  20.  For 
20  give  the  name  twenty  (twain-ty,  twain  being  two 
and  ty  ten). 

Let  the  pupils  suggest  the  names  for  30  (three-ty 


SUGGESTIONS  TO   TEACHERS  xxiii 

or  thirty),  40,  and  so  on  up  to  90.  Ten  tens  he  will 
probably  call  ten-ty,  when  he  should  be  given  the 
new  name  one  hundred  and  so  on  with  the  other 
numbers  he  has  been  using. 

4.  Count    by   tens   the    number    of    fingers   and 
thumbs  of   the  children   in   the   first   row ;    of   the 
girls ;   of  the  boys.     Count  thus  :    1  ten,  2  tens,  3 
tens,  4  tens,  5  tens,  6  tens  or  60,  i.e.  6  tens  and  no 
units. 

5.  Give  exercises  in  counting  by  tens  from  a  clock 
face.     Count  from  XII  to  VI  from  right  to  left  and 
from  left  to  right.     Count  from  XII  around  to  XII 
again. 

6.  What  is  the  temperature  in  the  schoolroom  at 
10.30  A.M.?     What  is  it  outside?     Answer  thus: 
6  tens  and  8°  and  gradually  change  to  68°,  i.e.  6  tens 
and  8  units.     Continue  this  work  from  day  to  day. 

7.  Note    the    time    on    the    clock   face    counting 
by  tens  and   minutes,   for   instance,    2   tens  and  3 
minutes  after  9  o'clock.      Change  gradually  to  23 
minutes  after  9  o'clock,  i.e.  2  ten  minutes  and  3 
minutes. 

8.  Measure  certain  distances  with  a  metric  stick ; 
for   instance,    this  distance   is   2   meters,  that  is  4 
meters,  and  so  on.     This  distance  is  1  meter  6  deci- 
meters ;    that,  2  meters  4  decimeters.     Again,  this 
distance  is  2  meters  1  decimeter  5  centimeters  ;  that, 
3  meters  5  decimeters  8  centimeters,  and  so  on. 

9.  Count  the  number  of  centimeters  in  a  deci- 


xxiv  SUGGESTIONS  TO   TEACHERS 

meter.  One  decimeter  is  equal  to  10  centimeters, 
i.e.  1  decimeter  and  no  centimeters.  Two  decime- 
ters equal  20  centimeters,  i.e.  2  decimeters  and  no 
centimeters;  and  so  on.  Nine  decimeters  equal  90 
centimeters,  i.e.  9  decimeters  and  no  centimeters. 

10.  One  decimeter  1  centimeter  is  equal  to  11 
centimeters,  i.e.  1  decimeter  1  centimeter.  One 
decimeter  2  centimeters  is  equal  to  12  centimeters, 
i.e.  1  decimeter  2  centimeters;  and  so  on.  One 
decimeter  9  centimeters  is  equal  to  19  centimeters, 
i.e.  one  1  decimeter  9  centimeters. 

So  with  2  decimeters  1  centimeter,  2  decimeters 
2  centimeters,  and  so  on,  as  continuously  as  necessary, 
up  to  9  decimeters  9  centimeters. 

Test  thus  :  2  decimeters  4  centimeters  =  ?  centime- 
ters ?  65  centimeters  =  ?  decimeters  and  centimeters  ? 

11.*  Count  the  number  of  decimeters  in  a  meter. 
One  meter  is  equal  to  100  centimeters,  i.e.  1  meter 
no  decimeters  no  centimeters.  Two  meters  is  equal 
to  200  centimeters,  i.e.  2  meters  no  decimeters  no 
centimeters,  so  on  up  to  9  meters. 

One  meter  1  decimeter  is  equal  to  110  centimeters, 
i.e.  1  meter  1  decimeter  no  meters.  One  meter  2 
decimeters  is  equal  to  120  centimeters,  i.e.  1  meter 
2  decimeters  no  centimeters,  and  so  on  up  to  1  meter 
9  decimeters,  and  so  on  as  continuously  as  necessary 
up  to  9  meters  9  decimeters. 

*  This  notation  need  not  be  extended  beyond  99,  unless  thought 
desirable,  until  after  Lesson  14, 


SUGGESTIONS  TO  TEACHERS        XXV 

One  meter  1  decimeter  1  centimeter  is  equal  to 
111  centimeters,  i.e.  to  1  meter  1  decimeter  2  centi- 
meters. 

Develop  112,  113,  114,  etc.,  121,  122,  123,  etc., 
as  continuously  as  necessary  up  to  999. 

Test  thus  :  5  meters  4  decimeters  8  centimeters  is 
equal  to  how  many  centimeters  ?  2  meters  6  centi- 
meters is  equal  to  how  many  meters  ? 

516  or  607  centimeters  is  -equal  to  how  many 
meters,  decimeters,  and  centimeters  ? 

In  the  above  work  use  contractions,  viz.  m  for 
meter,  dm  for  decimeter,  and  cm  for  centimeter. 

12.  Count  ten  pennies,  using  toy  or,  better,  real 
money.  What  coin  is  equal  to  ten  pennies  ?  Write 
the  sum  thus:  10^,  i.e.  1  dime  and  no  pennies. 
Similarly,  for  2  dimes  write  20^,  i.e.  2  dimes  and  no 
pennies,  and  so  on. 

Count  sums  of  money,  using  dimes  and  pennies. 
Write  the  results  thus:  12 £  i.e.  1  dime  2^;  46 £ 
i.e.  4  dimes  6^.  Test  the  work  as  before  in  §  10. 

Count  by  tens  from  0  to  90  (using  dimes  as  a 
basis),  from  1  to  91  (using  1  ^  and  dimes),  2  to  92 
(using  2  ^  and  dimes) ;  and  so  on. 

Count  ten  dimes.  What  coin  is  equal  to  ten 
dimes?  Write  the  sum  thus:  100^,  i.e.  $1,  no 
dimes,  no  pennies.  Similarly,  for  $  2  write  200  ^, 
i.e.  $2,  no  dimes,  no  pennies ;  and  so  on. 

Count  by  100's  from  0  to  1000.  Count  by  100's 
from  10  to  910;  11  to  911;  12  to  912  ;  and  so  on. 


XXVI 


SUGGESTIONS  TO  TEACHERS 


10 

20 

30 

40 

50 

60 

70 

80 

90 

11 

21 

31 

41 

51 

61 

71 

81 

91 

12 

22 

32 

42 

52 

62 

72 

82 

92 

13 

23 

33 

43 

53 

63 

73 

83 

93 

14 

24 

34 

44 

54 

64 

74 

84 

94 

15 

25 

35 

45 

55 

65 

75 

85 

95 

16 

26 

36 

46 

56 

66 

76 

86 

96 

17 

27 

37 

47 

57 

67 

77 

87 

97 

18 

28 

38 

48 

58 

68 

78 

88 

98 

19 

29 

39 

49 

59 

69 

79 

89 

99 

Count  by  10's  from  0  to  100 ;  0  to  300 ;  0  to  500 ; 
500  to  1000. 

13.  Have   the  pupils  name  and   write   down  all 
numbers  from  1  to  100  as  indicated  in  the  following 
table  : 

Write  the  upper  hori- 
zontal row  first  and 
then  fill  out  each  col- 
umn. 

Vary  the  exercise 
by  writing  the  first 
column  first  and  then 
construct  the  horizon- 
tal rows  in  succession. 
Let  the  children  simi- 
larly construct  the  200  table,  the  300  table,  and  so  on. 

14.  Review  Lessons  1-8  are  founded  on  the  above 
outline.     The  teacher  is  urged  in  this  connection  to 
read  the  PSYCHOLOGY  OF  NUMBER  and  especially 
Chapters  VIII  and  IX  on  Primary  Number  Teaching. 

IV.  Related  number  work.  —  Although  all  the 
work  suggested  in  the  foregoing  outlines  is  related 
to  the  normal  activities  and  experience  of  the  child, 
still  there  is  another  phase  of  related  number  work 
that  should  be  carefully  thought  out  and  systemati- 
cally developed  by  the  primary  teacher,  namely,  that 
in  which  number  is  distinctly  related  to  the  various 
occupations  of  the  schoolroom.  Its  purpose  is  the 
development  of  the  number  sense  rather  than 


SUGGESTIONS  TO   TEACHERS  xxvii 

acquiring  information  or  facility  in  number  manipu- 
lation. 

It  aids  in  laying  a  basis  for  future  work,  tends  to 
secure  exactness,  and  holds  the  child's  interest. 

It  may  be  grouped  under  four  headings  : 

1.    In  connection  with  the  school  administration. 

Thus  a  pupil  who  is  selected  to  pass  pencils  to  his 
row  of  six  pupils,  counts  out  the  number  he  needs, 
or  he  is  given  four  and  finds  that  he  is  two  short, 
or  eight  and  finds  that  he  has  two  too  many. 

2.*  In  connection  with  the  making  of  things, — 
involving  length,  surface,  weight,  size,  bulk.  An 
instance  of  this  is  given,  page  xiii,  §  11. 

3.*  In  connection  with  other  subject  matter, 
especially  science. 

4.  In  connection  with  number  games,  —  involving 
guessing,  comparison,  etc. 

*  "  One  Year's  Outlines  of  Work  in  First  Primary  Grades  "  by 
Flora  J.  Cooke  of  the  Chicago  Normal  School  is  suggestive* 


SUGGESTIVE   LESSONS 


I.  Counting 

See  Suggestion  under  Counting,  p.  xi.  (b.) 

CLASS.  Six  pupils,  Willie,  Charlie,  Frank,  Maud, 
Edna,  Edith. 

TEACHER.  Class,  we  shall  have  a  talk  to-day  about 
counting  chairs,  pencils,  and  other  things.  Charlie, 
which  is  the  tallest  pupil  in  the  class  ?  Edith  is. 

TEACHER.  Which  is  the  smallest  boy,  Edna? 
Willie  is. 

TEACHER.  Is  this  pointer  equal  to  Willie's  height, 
Frank  ?  I  can't  tell. 

TEACHER.  How  may  we  find  out,  Maud  ?  By 
putting  them  together. 

TEACHER.  Do  so,  Maud,  and  tell  me  which  is  the 
taller.  The  pointer. 

TEACHER.  Here  are  two  piles  of  blocks ;  which 
has  the  most,  Willie  ?  That  one. 

TEACHER.  Class,  how  shall  we  find  out  how  much 
larger  it  is?  Put  the  blocks  of  each  pile  on  top 
of  one  another,  and  see  which  is  the  higher  pile. 

TEACHER.  Charlie,  hold  this  apple  for  me.  How 
many  apples  has  Charlie,  Edith  ?  One. 

xxv  iii 


SUGGESTIVE  LESSONS 

TEACHER.  Edna,  hold  this  one.  How  many  has 
Edna,  Frank?  One. 

TEACHER.  Charlie,  give  yours  to  Edna.  How 
many  has  Edna  now,  Willie?  One  apple  and  one 
apple. 

TEACHER.  How  many  pairs  of  shoes  have  Willie  and 
Charlie  on  their  feet,  Maud  ?  One  pair  and  one  pair. 

TEACHER.  We  shall  get  some  chairs  now,  and  let 
you  sit  down.  Willie,  get  a  chair  and  sit  at  this  side 
of  the  table.  Charlie,  get  chairs  for  Frank  and 
yourself  to  sit  at  that  end.  How  many  chairs  must 
Charlie  bring,  Edith?  One  chair  and  one  chair. 

TEACHER.  Frank  will  bring  over  one  and  one 
chairs  for  all  the  girls  to  sit  at  the  side  ?  That  will 
not  be  enough. 

TEACHER.  Why,  Frank?  There  are  more  girls 
than  that. 

TEACHER.  Class,  how  many  girls  are  there  ? 
One  and  one  and  one. 

TEACHER.  How  many  chairs  shall  Frank  bring, 
then,  Maud  ?  One  and  one  and  one. 

TEACHER.  How  many  thumbs  at  this  end  of  the 
table,  Willie  ?  One  and  one. 

TEACHER.  Wouldn't  you  like  a  shorter  way  of 
naming  the  one  and  one,  class  ?  Yes. 

TEACHER.  Well,  we  name  the  one  and  one,  two. 
Frank,  how  many  eyes  have  you  ?  Two. 

TEACHER.  How  many  eyes  have  Charlie  and 
Frank,  Maud  ?  Two  eyes  and  two  eyes. 


XXX  SUGGESTIVE  LESSONS 

TEACHER.  How  many  cents  have  I  in  this  hand, 
Edna  ?  Two. 

TEACHER.    In  this  one,  Edith  ?     Two. 

TEACHER.    In  both,  Maud  ?     Two  two-cents. 

TEACHER.  How  many  girls  are  there,  Frank? 
One  and  one  and  one. 

TEACHER.  Edith,  you  move  your  chair  and  sit 
behind  Edna  and  Maud.  Willie,  tell  me  in  another 
way  how  many  girls  there  are  ?  Two  and  one. 

TEACHER.  Putting  Edith  first,  how  many  girls 
are  there,  Charlie  ?  One  and  two. 

TEACHER.  Willie,  you  sit  at  this  end  with  Charlie 
and  Frank.  How  many  pairs  of  shoes  have  the  boys, 
Edna  ?  Two  pairs  and  one  pair. 

TEACHER.  I  will  now  tell  you  a  shorter  name  for 
the  two  and  one.  We  call  the  two  and  one,  three. 
How  many  boys  in  our  class,  Edith  ?  Three. 

TEACHER.  How  many  boys  and  girls  in  our  class, 
Maud  ?  Three  boys  and  three  girls. 

TEACHER.  How  many  three-pupils  in  the  class, 
Charlie  ?  Two  three-pupils. 

TEACHER.  Willie,  count  the  girls,  beginning  with 
Edith.  One,  two,  three. 

TEACHER.  Beginning  with  Edna,  Frank.  One, 
two,  three. 

TEACHER.  I  want  a  boy  and  a  girl  to  sit  on  each 
side  of  the  desk.  How  many  on  all  sides,  Maud? 
Three  twos. 

TEACHER.    Charlie,  count  the  pairs  of   shoes  in 


SUGGESTIVE  LESSONS  Xxxi 

the  class.  One  two-pairs,  two  two-pairs,  three  two- 
pairs. 

TEACHER.  Frank  and  Maud,  please  move,  and  sit 
behind  Willie  and  Edna.  How  many  chairs  at  this 
end  of  the  table,  Edith  ?  Two  chairs  and  two  chairs. 

TEACHER.  How  many  ears  at  this  end,  Charlie  ? 
Two  two-ears  and  two  two-ears. 

TEACHER.  Frank,  move  in  front  with  Willie  and 
Edna.  Tell  me  in  another  way,  how  many  chairs  at 
this  end,  Edith.  Three  and  one. 

TEACHER.   Another  way,  Maud.     One  and  three. 

TEACHER.  A  shorter  way  of  saying  this  :  two  and 
two  is  four.  How  many  hands  have  Charlie  and 
Edith,  Willie  ?  Four. 

TEACHER.  Count  the  slates  at  this  end  of  the 
table,  Charlie,  beginning  with  Edna's.  One,  two, 
three,  four. 

TEACHER.  Beginning  with  Maud's,  count  the 
pencils,  Frank.  One,  two,  three,  four. 

TEACHER.  How  many  pupils  in  our  class,  Charlie  ? 
Four  and  two. 

TEACHER.  How  many  dresses  in  our  class, 
Willie  ?  Three. 

TEACHER.    How  many  coats  ?     Three. 

TEACHER.  How  many  suits  of  clothes  ?  Three 
and  three,  or  two  threes. 

TEACHER.  Class,  count  the  fingers  you  have  on 
one  hand,  leaving  out  the  thumb.  One,  two,  three, 
four. 


xxxii  SUGGESTIVE  LESSONS 

TEACHER.  Count  them  on  the  other  hand,  begin- 
ning with  the  little  finger.  One,  two,  three,  four. 

TEACHER.  Counting  the  thumb  with  the  four 
fingers,  how  many  in  all,  Edna?  Four  and  one. 

TEACHER.  Putting  your  hands  together,  finger  to 
finger  and  thumb  to  thumb,  how  many  on  both 
hands,  Maud  ?  Four  twos  and  one  two. 

TEACHER.    Four  and  one  is  called  five. 

(Give  exercises  on  five,  and  then  give  the  name 
six,  etc.). 

II.  Measuring 

(Lesson  in  Number  given  to  first  grade  pupils) 

The  children  are  rejoicing  in  the  possession  of 
their  new  books,  slates,  and,  above  all,  rulers.  First 
grade  pupils  always  want  rulers,  probably  because 
they  see  them  in  use  in  the  higher  grades.  The 
children  come  with  brand  new  foot  rulers,  joy  in 
their  hearts  and  on  their  faces ;  for  the  teacher  has 
told  them  that  to-day  they  are  to  have  their  first  les- 
son in  measuring,  and  therefore  will  have  a  chance  to 
use  their  treasures.  The  teacher  has  provided  many 
different  colored  slips  of  paper,  varying  in  length 
from  one  foot  to  six  feet  (no  inches  used  to-day), 
which  the  children  are  to  measure ;  also  long  slips 
of  paper,  tape,  or  ribbon  rolled  up  into  a  ball  from 
which  different  lengths  can  be  cut.  "  Now,  children, 
we  shall  measure  so  many  things  to-day,  all  these 


SUGGESTIVE  LESSONS  xxxiii 

bright  pieces  of  paper,  our  aprons,  and  desks,  and 
we  want  to  see  how  tall  the  littlest  girl  is.  Who  is 
the  littlest  girl,  do  you  think  ?  "  (Class  unanimous 
in  favor  of  Violet.)  "  Very  well ;  we  will  measure 
Violet,  and  I  think  some  one  had  better  measure  me. 
I  want  to  know  how  tall  I  am."  (Hands  wave  fran- 
tically in  the  air.)  "But  first  we  must  know  how 
long  our  rulers  are ;  hold  them  up  straight  in  front 
of  you  to  see  if  they  are  all  the  same  length."  (Cries 
of  Yes,  yes.)  ^  "  Well,  how  long  is  that,  Katie  ? " 
(Katie  does  not  know.)  "  Charlie,  do  you  know  ?  " 
"Yes,  it's  one  foot."  "Right,  Charlie.  Now  chil- 
dren, how  long  is  each  ruler  ?  "  "  One  foot."  "  Now 
let  us  measure  this  pretty  slip  of  blue  paper  first." 
(Ethel  measures  and  finds  it  to  be  one  foot.)  "  This 
piece."  (Hazel  measures  and  finds  it  to  be  one 
foot.)  "  Surely  we  have  some  longer  pieces.  Who 
is  a  good  enough  guesser  to  find  me  a  piece  about 
two  feet  long,  a  piece  twice  as  long  as  the  ruler  ?  " 
(Charlie  holds  up  a  piece.)  "  Well,  Charlie,  measure 
it  and  let  us  see  if  you  guessed  right."  (Children 
anxiously  watch  the  measuring.)  "  Was  he  right, 
children?  "  (Cries  of  Yes,  yes.)  "  How  long  is  it  ?  " 
"Two  feet."  "Now  I  shall  give  each  one  of  you  a 
slip  on  your  desk  ;  let  me  see  who  can  measure  the 
most  carefully."  (During  the  few  moments  that  this 
measuring  is  going  on,  the  teacher  passes  quickly 
from  child  to  child  in  order  to  see  that  each  one 
understands  thoroughly  what  he  is  doing,  questions 


XXxiv  SUGGESTIVE  LESSONS 

here  and  there  regarding  the  color  of  the  paper, 
comparing  the  piece  on  one  desk  in  color  and  length 
to  that  on  another  desk,  etc.,  etc.)  "I  see  you  all 
understand  that  very  well  indeed. 

"  Now  I  believe  you  can  measure  well  enough  to 
see  how  tall  I  am."  (Cries  of  Oh  yes,  we  can,  we 
can.)  "  Well,  I  am  going  to  choose  a  nice  soft  ruler 
and  have  some  quiet  child  measure  me."  (Children 
try  to  look  decorous.)  "  Well,  George,  you  try." 
(George  carefully  measures  the  teacher's  height, 
while  class  looks  on  in  breathless  interest.)  "Well, 
Katie,  how  tall  am  I  ? "  "  Please,  I  counted  four 
feet."  "Hazel?"  "I  counted  five  feet."  (Most 
of  the  class  answer  five  feet.)  "Well,  George,  try 
again  and  then  tell  me."  After  another  careful 
measurement  the  class  decide  that  the  teacher  is  five 
feet  and  a  "little  bit  more."  "Very  well,  we  shall 
not  say  anything  about  this  little  bit  more  to-day  ; 
some  other  day  we  shall  talk  about  that ;  we  will  say 
that  I  am  five  feet.  Now  let  us  measure  Violet ; 
Mary,  you  try."  Violet  is  measured  and  found  to 
be  four  feet.  Similarly  the  tallest  boy  is  measured, 
Hazel's  beautiful  golden  hair,  the  ribbon  that  ties  it, 
the  teacher's  apron,  etc.,  etc.  (All  this  measuring  is 
done  by  repeating  the  unit  of  measurement  one  foot; 
it  may  be  a  foot  of  soft  ribbon  or  a  slip  of  paper 
or  the  ruler,  but  it  is  the  same  unit  all  the  way 
through.) 

"Now,  children,  we  shall  have  some  cutting  and 


SUGGESTIVE   LESSONS  XXXV 

measuring,  too."  (Holding  up  and  unwinding  the 
ball  of  colored  paper.)  "I  want  some  one  to  come 
and  cut  off  exactly  a  foot."  (John  measures  a  foot 
very  carefully  and  as  carefully  cuts  it  off.)  "  Give 
that  to  Mary ;  she  wants  it  for  a  sash  for  her  doll. 
Is  that  enough,  Mary  ?  "  (Mary  answers  No,  so  John 
cuts  her  two  feet  more.)  "  Now,  children,  how  many 
feet  has  Mary  altogether  ?"  "She  has  three  feet." 
"  How  many  did  she  have  first  ?  And  then  how 
many  ?  How  many  does  that  make  ?  Very  well,  I 
want  some  one  to  make  a  picture  on  the  blackboard 
to  show  how  many  feet  of  ribbon  or  paper  Mary 
has."  (Some  child  comes  to  the  blackboard  and 
draws  something  like  this:  |  |  |  .)  "That  is  very 
well,  but  sometimes  we  just  make  little  dots  like 
this  "  (making  three  dots  on  the  blackboard,  thus  \*). 
"  Now,  Katie,  come  and  show  us  with  dots  how  many 
feet  of  ribbon  Mary  has.  Let  us  give  Joe  some 
ribbon  now  for  the  tail  of  his  kite  ;  cut  him  three 
feet,  Ethel."  (Ethel  cuts  three  feet,  measuring  with 
ruler.)  "He  says  that  is  not  enough,  Ethel;  give 
him  two  feet  more.  How  much  has  he  now,  chil- 
dren ?  "  Nearly  every  child  will  answer  five  ;  those 
who  do  not  know  may  count.  Teacher  may  drill 
by  getting  Joe  to  hold  the  three  pieces  in  one 
hand,  the  two  in  the  other,  by  making  three  colored 
dots  and  two  white  ones,  thus  *•*,  or  by  drawing  a 
line  between  them,  thus  ~i~.  Many  little  devices 
will  present  themselves  to  the  mind  of  the  teacher. 


XXXVI  SUGGESTIVE  LESSONS 

She,  too,  will  learn  by  doing.  It  is  better  not  to  con- 
fine oneself  to  the  combinations  of  any  particular 
number  during  the  first  lessons,  and  it  may  be  well 
not  to  have  any  addition  at  all,  but  simply  the  meas- 
urements. At  any  rate,  no  effort  should  be  made  at 
this  early  stage  to  memorize  the  combinations.  In  a 
similar  way  may  the  yard  and  the  inch  unit  of  meas- 
urement be  introduced.  This  lesson  is  spoken  of  as 
the  first  lesson.  Much  has  been  gained  if  during 
this  time  the  child  has  learned  to  measure  with  the 
units  of  measurement  —  the  inch,  the  foot,  and  the 
yard  —  and  got  an  idea  of  the  use  of  Number. 

III.  Counting  and  Measuring 

Suggestions  for  teaching  the  relation  of  3  to  2  and 
4,  5  to  4  and  6,  7  to  6  and  8,  etc. 

After  the  pupil  has  a  good  working  idea  of  2,  and 
has  been  drilled  in  constructive  exercises  in  twos 
and  groups  of  twos,  he  will  have  a  fair  idea  of  four, 
as  two  twos,  but  to  reach  a  complete  idea  of  four  the 
pupil  must  pass  through  the  number  three,  i.e.  he 
must  learn  3  as  1  more  than  2,  and  1  less  than  4. 
Similar  remarks  apply  to  5,  7,  and  9. 

To  teach  3,  or  5,  or  7,  etc. 

Give  constructive  exercises  in  which  the  numbers 
2,  or  4,  or  6,  as  the  case  may  be,  are  prominent,  but 
in  which  the  ideas  of  3,  or  5,  or  7,  are  present.  E.g. 
with  these  splints  (6)  construct  two  triangles,  and 
then,  with  the  same  number  of  splints,  make  as  many 


SUGGESTIVE   LESSONS  XXXvii 

pickets  as  possible.  Having  done  so,  question  the 
class  as  to  the  number  of  splints  it  requires  to  make 
a  triangle,  viz.  two  and  one.  How  many  pickets 
were  made  ?  Two  and  one.  Similarly  treat  5  in  its 
relation  to  4,  etc. 

Many  such  constructive  exercises  will  show  the 
relation  of  three  to  two,  viz.  as  one  more  than  two, 
or  two  and  one ;  now,  to  show  its  relation  to  4,  con- 
struct a  square  with  these  splints  (4).  How  many 
splints  did  you  use  ?  Two  twos  or  two  and  two  ? 
Construct  another  with  these  (3).  Pupils  cannot 
do  it.  It  takes  2  twos  to  make  a  square.  They 
have  1  less  than  2  twos,  or  two  and  1,  as  before. 

Having  given  many  constructive  exercises  on  three 
in  this  way,  with  splints,  blocks,  measures,  etc.,  the 
name  three  may  be  given  as  a  more  convenient  way 
of  saying  two  and  one,  and  one  less  than  two  twos 
(the  expression  two  twos  being  used  as  the  name 
four  has  not  yet  been  given). 

The  name  three  having  been  given,  drill  should 
be  given  in  constructive  exercises  in  which  threes 
and  groups  of  threes  are  prominent,  and  four  should 
now  be  taught  as  3  and  1,  and  the  name  four  given. 

When  the  pupil  knows  3  thoroughly,  he  really 
knows  6  as  2  threes,  and  as  he  knows  4  also,  the  in- 
termediate number  5  may  be  taught  as  3  has  been. 

After  plenty  of  drill  with  different  units  of  meas- 
ure and  groups  of  units  of  measure,  the  number- 
picture  for  3  J  •  may  be  given,  in  which  the  dots 


XXXVlii  SUGGESTIVE   LESSONS 

may  represent  any  unit  of  measure,  and  the  symbol, 
3,  may  now  be  introduced  in  association  with  its 
number-picture,  and  this  will  serve  to  impress  both 
idea  and  symbol  on  the  mind. 

IV.  The  Tens 

"  Who  was  it  came  in  late  this  morning,  John,  and 
spoiled  our  nice  clean  record  ? "  John  being  the 
culprit  hangs  his  head  and  says  nothing.  "  Can 
any  one  tell  me  how  late  John  was  ? "  (Various 
answers  are  given  ;  the  teacher,  however,  accepts  the 
"  few  minutes  "  answer,  as  the  five  minute  is  the  unit 
of  measure  desired  for  this  lesson.)  "  Well,  some  of 
you  are  almost  right,  but  I  will  tell  you  exactly  :  he 
was  just  five  minutes  late  ;  but  how  do  you  think 
I  knew,  Katie?"  "I  saw  you  look  at  the  clock." 
"Let  us  all  look  at  the  clock."  (Holding  up  clock 
or  paper  clock  face  with  hands  that  turn  easily,  see 
how  many  marks  it  has  to  tell  time  by.)  Let  us 
begin  at  one  and  count.  The  class  counts  from  I  to 
XII,  it  being  understood,  of  course,  that  the  children 
are  not  expected  to  learn  these  Roman  numerals,  ex- 
cepting, perhaps,  I,  II,  III,  IIII,  and  possibly  X ; 
that  is,  no  special  effort  should  be  made  to  learn 
them. 

"  Very  well ;  I  see  you  can  count  to  twelve ;  now 
what  do  you  call  these  little  things  that  point  to  the 
marks  so  that  we  may  know  which  one  to  take  ? 
Well,  this  big  hand  is  the  one  that  told  me  about 


SUGGESTIVE  LESSONS  XXXIX 

John's  being  five  minutes  late.  Now  you  see  it  is  just 
nine  o'clock  "  (moving  hands  to  that  time).  "  Who 
can  move  this  big  hand  so  that  it  will  be  five  minutes 
later  than  nine  ? "  (Katie  moves  it  a  five-minute 
space.)  "Very  well,  move  it  five  minutes  more, 
Ethel ;  five  minutes  more,  Charlie ;  five  more,  John. 
I  see  you  all  know  that  from  one  big  mark  to  another 
makes  five  minutes.  Now  I  want  you  all  to  count 
while  I  move  the  big  hand,  to  see  if  you  can  tell  how 
many  5's  I  go  over."  (Moves  hand  slowly  from  XII 
to  I ;  children  count  as  one  five  from  I  to  II ;  chil- 
dren count  two  5's  from  II  to  IV  ;  children  count 
three  5's,  etc.,  etc.)  The  teacher  drills  well  on  count- 
ing the  5's  before  touching  upon  the  hour  or  the 
minute  unit  of  measurement,  and  before  counting  the 
10's.  The  counting  (10's  and  by  10's)  from  a  clock 
face  may  be  taken  up  somewhat  as  follows : 

The  teacher  has  a  paper  clock  face ;  the  children 
know  that  from  one  big  mark  (called  big  to  dis- 
tinguish it  from  the  little  minute  mark  which  is  to 
be  taken  up  later)  to  another  there  is  one  5 ;  e.g. 
"  If  I  move  this  minute  hand  from  XII  to  I,  how 
many  5's,  children?"  "One  five."  "If  I  move  it 
from  I  to  II?"  "Two  5's."  "Five  minutes  and 
five  minutes.  Make  a  picture  of  that  in  dots, 
Charlie."  (These  pictures  have  become  familiar  to 
them  in  previous  lessons,  so  Charlie  at  once  makes 
*•*  *•*  and  the  class  at  once  recognizes  it  as  10.) 
"  Very  well,  indeed ;  now  I  shall  put  a  little  red 


xl  SUGGESTIVE  LESSONS 

mark  at  this  ten-minute  place  "  (making  red  stroke  at 
II  on  the  paper  clock  face),  "  so  as  not  to  lose  it,  for 
we  want  to  count  10's  now  if  we  can.  Dora,  come 
and  move  this  big  hand  ten  minutes  more ;  how 
many  5's  must  you  have,  Dora  ?  "  (Dora  moves  the 
hand  from  II  to  III  I,  and  the  teacher  puts  another  red 
stroke  to  indicate  10  minutes  more,  and  so  on  until 
the  six  tens  are  each  indicated  by  the  red  stroke. 
The  class  then  counts  the  10's  from  the  one  first 
marked  to  the  one  last  marked,  from  the  last  to  the 
first,  and  in  every  conceivable  way,  understanding 
all  the  time  that  any  two  five  minute  spaces,  no  mat- 
ter what  their  position  as  regards  the  big  marks, 
make  ten  minutes.  Then  they  count  from  the  clock 
face,  from  the  paper  face  with  the  strokes  erased, 
etc.,  etc.  In  this  counting  by  10's,  ten-cent  pieces 
may  be  used  to  good  advantage.) 

In  introducing  the  minute  unit  of  measurement, 
some  such  plan  as  the  following  may  be  adopted : 
"Now,  children,  here  is  our  face  again.  We  have 
been  talking  all  the  time  about  these  big  marks" 
(pointing  to  XII,  I,  II,  III,  etc.).  "How  many  are 
there  ?  "  ("  Twelve,  twelve.")  "  Oh,  I  see  you  all 
know  that ;  well,  now  I  want  you  to  put  on  your 
spectacles  and  see  if  you  can  find  me  any  little 
marks.  Well,  Dora,  show  them  to  me.  Now,  count 
how  many  there  are  from  I  to  II."  Dora  counts 
five.  "  Now,  children,  what  does  each  of  these  little 
marks  show  ?  "  "  One  minute,"  These  minute  marks 


SUGGESTIVE   LESSONS  xli 

may  have  been  introduced  in  the  lesson  on  the  five- 
minute  unit  of  measurement,  but  as  it  is  better  at 
first  to  deal  with  but  one  unit  of  measurement  at  a 
time,  it  is  supposed  that  if  there  has  been  any  men- 
tion of  these  minute  marks,  it  was  merely  a  casual 
mention ;  the  time  has  now  come  for  giving  atten- 
tion to  them. 

"  Now,  children "  (taking  up  the  clock  face  with 
the  10  minute  spaces  indicated  by  the  red  strokes), 
"  let  us  see  if  we  were  right  when  we  marked  these 
ten  minutes  ;  count  the  minute  marks."  Children 
count  the  minute  marks  in  each  10  minute  space, 
and  agree  that  the  strokes  were  correctly  placed. 
"Now,  let  us  count  10's  once  all  the  way  round." 
(Class  counts,  "  one  ten,  two  tens,  three  tens,  four 
tens,  five  tens,  six  tens,  or  sixty")  "Very  well; 
now  the  minute  hand  is  going  on  a  journey,  but  I 
am  going  to  make  him  run  so  fast  that  he  will  have 
to  rest  quite  often ;  when  he  stops  to  rest,  you  call 
out  the  name  of  the  station "  (turns  hand  quickly 
from  XII  to  II).  (Class  calls  out,  "One  10.") 
"  That  is  right ;  now  this  station  ? "  (turning  hand 
from  II  to  IIII).  (Class  calls  Two  10's.)  "  Good  ; ' 
but  can  any  one  tell  me  what  other  name  this  station 
has  ;  two  tens  are  how  many  ?  "  Perhaps  some  child 
can  tell.  If  not,  the  teacher  counts  with  them,  two 
10's  or  twenty  minutes,  three  10's  or  30  minutes, 
four  10's  or  40  minutes,  five  10's  or  50  minutes,  six 
10's  or  60  minutes.  "  And  what  do  you  think,  chil- 


SUGGESTIVE   LESSONS 

dren,  this  last  station  has  another  name  yet ;  it  has 
three  names.  It  has  the  same  name  as  the  little 
hand  ;  now  you  know."  (Some  one  in  the  class 
will  say  hour.)  "  That  is  good ;  now  let  us  say 
all  together  the  three  names  of  this  station,  "Six 
tens  or  sixty  minutes  or  one  hour." 

Of  course,  much  drill  will  be  necessary  and  much 
variety  in  the  modes  of  presentation.  The  dollar 
may  be  taught  in  the  same  way  with  ten-cent  pieces 
as  unit  of  measurement,  e.g.  one  ten,  two  tens,  or  20 
cents,  three  tens  or  30  cents  .  .  .  ten  tens  or  100 
cents  or  one  dollar.  So  also  with  metric  units.  After 
a  thorough  drill  in  lessons  of  this  kind,  there  will  be 
very  little  difficulty  in  such  lessons  as  are  indicated 
in  "Suggestion"  III,  13.  Practical  questions  are,  of 
course,  given  as  soon  as  possible,  e.g.  If  I  am  five 
feet  tall  and  Violet  is  four  feet,  how  much  taller  am 
I  than  Violet?  Katie's  ribbon  is  six  feet,  Violet's 
piece  is  two  feet.  How  many  times  can  Violet's  be 
cut  out  of  Katie's  ?  Mary  has  20  cents  ;  how  many 
oranges  can  she  buy  if  one  cost  5  cents  ?  How  many 
minutes  in  one  hour  ?  in  one-half  hour  ?  How 
"many  ten-cent  pieces  in  fifty  cents  ?  How  many 
dollars  in  6  ten-dollar  bills  ?  etc. 

V.  Constructive  Exercises 

The  importance  of  constructive  exercises  in  teach- 
ing arithmetic  will  be  evident  if  we  keep  in  view 
that  number  is  the  instrument  of  measurement,  and 


SUGGESTIVE  LESSONS  xliii 

as  such  contains  three  factors  ;  viz.  the  vague  whole 
of  quantity  to  be  measured,  the  unit  of  measure- 
ment, and  the  times  of  its  repetition  to  measure  or 
equal  the  whole  quantity. 

This  necessitates  from  the  very  first  exercises  in 
parting  (breaking  up  or  measuring  off  into  units  of 
measure)  and  wholing  (putting  together  or  relating 
these  units  to  equal  the  whole). 

Hence,  for  a  short  time  the  beginner  may  be  exer- 
cised in  constructive  acts  without  formal  drill  on  the 
how-many  idea.  For  example  :  breaking  up  a  large 
cube,  composed  of,  say,  three  small  blocks,  into  its 
parts,  and  putting  them  together  again.  Breaking 
up  and  forming  triangles,  pickets,  squares,  lines,  etc. 

Having  spent  some  time  in  such  work,  the  num- 
bers may  be  introduced  gradually;  thus,  one  and  one 
splint  make  one  picket,  one  picket  and  one  picket, 
two  pickets,  two  splints  and  one  splint  make  a  tri- 
angle, two  twos  make  a  square,  etc.  Thus  the  need 
for  a  certain  number  in  each  case  is  shown,  and 
children  see  the  use  and  value  of  number.  Such 
exercises  as,  Construct  a  cube  with  8  blocks,  or  rec- 
tangular "  bricks "  of  given  dimensions,  according 
to  the  advancement  of  the  child,  also  show  the  value 
of  number. 

Then,  in  addition  and  subtraction,  such  exercises 
as :  The  edge  of  a  slate  is  measured  by  the  parts  5 
inches  and  6  inches.  How  long  is  the  slate  ? 

A  pail  is  measured  by  a  pint  measure,  a  2-pint 


xliv  SUGGESTIVE   LESSONS 

measure,  and  an  8-pint  measure.  How  many  pints 
does  the  pail  hold?  etc.  Let  the  children  take  the 
actual  units  and  do  the  measuring,  for  a  time  at 
least,  until  the  operation  is  thoroughly  familiar. 

In  multiplication  and  division  : 

How  many  square  inches  in  a  rectangle  which  is 
9  in.  long  and  3  in.  wide?  Construct  such  a  rec- 
tangle, or  rather  let  the  class  construct  it,  and,  in 
fact,  whatever  new  idea  you  are  introducing,  do  it 
by  use  of  constructive  exercises,  and  thus  let  the 
child  actually  see  the  meaning  and  use  of  the  dif- 
ferent operations.  Now,  let  the  inch  stand  for  foot. 
What  is  the  problem  ?  The  result  ? 

How  many  cords  of  wood  in  a  pile  16  ft.  long,  8  ft. 
high,  and  4  ft.  wide?  Construct  such  a  pile,  using 
cubic  inches  to  represent  cubic  feet. 

How  many  yards  of  carpet,  or  how  many  rolls  of 
paper,  will  be  required  for  a  room  ?  Use  strips  of 
colored  paper  or  pasteboard  to  represent  strips  of  car- 
pet or  paper,  and  place  these  side  by  side  on  a  larger 
piece  of  cardboard  which  represents  the  floor  or  wall 
of  the  room. 

VI.  The  Two  Measurements 

First  by  simple  constructive  exercises  show  that 
one  measurement  carries  with  it  a  related  one. 

Measure  a  6-inch  line  by  a  2 -inch  measure,  then 
by  a  3-inch  measure,  and  from  the  class  get  their 
result  in  the  form  that  3  times  2  inches  equals  6 


SUGGESTIVE  LESSONS 


inches,  and  2  times  3  inches  equals  6  inches,  and  then 
in  the  form  3  times  2  in.  =  2  times  3  in.  =  6  in.,  or 
2  x  3  in.  =  3  x  2  in.  =  6  in.  Show  with  dots. 

Then  with  blocks,  cubic  inches,  3x2  cu.  in.  = 
2x3  cu.  in.  =  6  cu.  in.  Use  many  units  of  measure 
until  you  lead  the  class  to  see  that  3x2  units  = 
2x3  units  =  6  units ,  whatever  unit  of  measure 
may  be  used. 

Similarly  with  other  sets  of  factors,  as  4x8  = 
8  x  4  =  32,  etc. 

Having  thus  shown  that  this  "  law  of  commutation  " 
is  true,  simple  problems  may  be  worked  out,  showing 
how  it  is  true,  and  the  use  of  this  essential  principle. 
Give  such  a  problem  as  : 

I.  A  rectangular  piece  of  board  (actually  present 
the  board  to  the  class)  is  6  in.  wide  arid  8  in.  long. 
How  many  square  inches  does  the  surface  measure  ? 
(Cover  this  board  with  square  inches  made  of  card- 
board.) 

Using  horizontal  row  as 
unit  of  measure,  what  is 
the  number  ? 

Using  a  vertical  row  as 
unit  of  measure,  what  is 
the  number  ? 

It  follows  that  8  x  6  sq.  in. 
=  6  x  8  sq.  in. 
This  is  probably  the  simplest  application  of   the 
law  of  commutation. 


xlvi  SUGGESTIVE  LESSONS 

II.    Among  3  boys  a  number  of  pennies  are  divided, 
giving  6  to  each.     How  many  pennies  were  there  ? 
•  •••••  first  six.          Let   the  dots   on   the   board 


second  six. 


represent  the  pennies.     I  may 

third  six.         ,..,', 

divide  these  pennies  in  one  of 
>  |  £  a  *  §  two  ways,  and  it  is  immaterial 


^ 


' 


which  way  I  divide  them. 

«/ 


I  may  give  the  first  boy 


A  whole  of  3  sixes  or  6  threes.     his    wh()le 

the  second  boy,  etc.  In  that  case  I  should  have  6 
cents  taken  3  times  =  3x6  cents  =  18  cents. 

(b)  Again,  I  may  give  a  cent  to  the  first  boy,  an- 
other to  the  second,  and  another  to  the  third,  making 
a  whole  of  3  cents.  This  may  be  repeated  6  times, 
making  in  all  6  times  3  cents  =  18  cents. 

The  operations  are  identical,  but  viewed  from  two 
standpoints. 

VII.  Fractions 

1.  Let  pupils  measure  a  foot  line  with  a  6  in.,  4  in., 
3  in.,  2  in.,  1  in.,  and  ^  in.  measure.  Hence,  have 
pupils  draw  6  lines,  each  a  foot  long,  and  mark  them 
off  with  these  units.  How  many  equal  parts  in  the 
first  line  ?  Two.  One  of  these  is  one  out  of  how 
many  ?  How  many  equal  parts  in  the  second  line  ? 
Three.  One  part  is  one  out  of  how  many  ?  Two 
are  two  out  of  how  many?  etc.,  etc.  This  is  how 
we  express  one  out  of  two  :  ^  ft.  Ask  class  to  show 
how  to  express  1  out  of  3,  4,  5,  .  .  .  100,  x. 


SUGGESTIVE  LESSONS  xlvii 

2.  How   many   equal    parts   in   the    third    line  ? 
Four.     Show  how  to  express  one  of  these.    ^.    Now, 
we  wish  to  express  2  out  of  4,  instead  of  1  out  of  4  ; 
how  shall  we  do  so  ?     By  putting  2  in  place  of  the  1. 
f  .     Express  3  out  of  4,  4  out  of  4,  7  out  of  12,  8  out 
of  24,  etc. 

3.  From  this,  draw  from  the  class  that  1  part  of 
the  first  line  is  J  of   the  whole,  2  parts,  |,  or  the 
whole  line  ;  1  part  of  the  second  line  is  J  ;   2  parts, 
|-;  3  parts,  j,  or  the  whole  line  ;  etc.,  etc.     Finally, 


1  =  T42  =  28^  etc.     From  many  other  examples,  lead 
pupils  to  tell  you  that 


12345  » 

•|=|=I32=-5^=   .  .  .  ad  inf.;  etc.,  etc. 

4.  The  meaning  of  the  numerator  and  denomi- 
nator may  now  be  impressed  more  strongly  on  the 
pupils'  minds.  Thus:  What  is  the  name  of  each 
part  in  the  fourth  line  ?  A  sixth.  Express  1  part,  3 
parts,  6  parts.  ^,  f  ,  f  .  Express  4  parts  of  the  last 
line.  2T'  e^c-  What  does  the  denominator  of  each 
fraction  tell  us  ?  The  name  of  the  part  and  the  size 
of  it.  Again,  in  the  fifth  line,  what  is  the  name  of 
each  part  ?  A  twelfth.  What  is  the  number  of  such 
parts  in  the  whole  line  ?  12.  How  many  such  parts 
in  l  the  line  ?  6.  Express  the  6  parts  ?  -f%.  What 
does  the  12  tell  ?  The  name.  What  does  the  nu- 


xlyiii  SUGGESTIVE  LESSONS 

merator  tell?     The  number  of  parts  that  make  up 
the  quantity.     Give  many  other  examples. 

5.  Give  a  pupil  a  strip  of  cardboard  and  ask  him 
to  cut  off  a  piece  of  it,  equal  to  one  of  the  parts  in 
the  third  line.  How  long  is  this  strip  of  cardboard  ? 
£  ft.  Use  it  to  measure  each  of  these  lines  that  I 
have  drawn  (9  in.,  1  ft.,  1^  ft.,  2J  ft.,  etc.,  any 
length  whatever).  How  many  parts  in  each  ?  3,  4, 
5,  10,  etc.  What  is  the  name  of  each  part  ?  ^  ft. 
How  long,  then,  is  the  first  line  ?  f  ft.  The  second? 
f  ft.  The  third?  |  ft.  The  fourth?  ^  ft.,  etc. 
Use  many  other  examples. 

NOTE.  —  The  five  points  developed  above  have  been,  for 
brevity,  developed  by  means  of  lines  only.  Teacher  should  use 
many  other  units,  as  TV  of  a  dollar,  T^  of  an  hour,  etc.,  etc. ;  e.g. 
show  that  40  cents  is  4  dimes  or  y4<y$;  $1.30  is  13  dimes  or  |f  $, 
and  so  on.  Fractions  are  thus  simply  another  way  of  express- 
ing numbers  that  pupils  have  handled  from  the  first. 

VIII.  Number  =  The  Tool  of  Measurement 

TEACHER.  To-day,  boys  and  girls,  let  us  have  a 
little  talk  on  buying  and  selling,  measuring  and 
counting,  etc.,  with  a  view  to  finding  out  why  such 
processes  are  carried  on.  For  example,  why  do  peo- 
ple in  buying  butter  measure  (weigh)  it  ?  And  why 
is  it  dear  at  one  season  and  cheap  at  another  ? 

PUPIL.  Because  butter  is  got  only  by  hard  work, 
and  because  it  is  more  plentiful  at  one  time  than 
another. 


SUGGESTIVE  LESSONS  xlix 

TEACHER.    How  is  butter  generally  sold  ? 

PUPIL.    By  the  pound. 

TEACHER.    Well,  how  do  we  generally  buy  butter  ? 

PUPIL.    With  money. 

TEACHER.  When  people  are  selling  butter,  are 
they  very  particular  about  weighing  it  (whether 
they  are  giving  more  than  a  pound  or  not)? 

PUPIL.    Yes. 

TEACHER.  When  people  are  buying  butter  do 
they  always  like  to  get  it  as  cheap  as  possible,  or 
will  a  few  cents  more  make  any  difference  ? 

PUPIL.    Yes. 

TEACHER.  Well,  let  us  consider  the  question 
from  the  buyers'  and  the  sellers'  standpoint,  and  dis- 
cover what  makes  a  transaction  a  fair  one.  First, 
why  is  the  farmer  so  particular  in  weighing  his 
butter  ? 

PUPIL.    Because  it  is  got  only  by  hard  work. 

TEACHER.  Now  let  us  consider  what  it  has  cost 
the  farmer  to  produce  butter.  Name  as  many  things 
as  you  can  that  go  to  make  up  the  cost. 

PUPIL.  He  must  buy  the  cows,  pay  for  their  feed 
and  attendance,  churn  the  butter,  bring  it  to  market, 
etc. 

TEACHER.  Well,  then,  do  you  think  it  right  that 
he  should  receive  some  remuneration  for  his  labor 
and  expense  by  charging  for  the  butter  ? 

PUPIL.    Certainly. 

TEACHER.    Well,  why  is  the  one  who  buys  the 


1  SUGGESTIVE  LESSONS 

butter  so  anxious  to  get  his  right  weight  and  also 
anxious  to  buy  as  cheaply  as  possible  ? 

PUPIL.  Because  he  has  to  work  hard  for  his  money, 
and  desires  therefore  to  make  it  go  as  far  as  possible. 

TEACHER.  Therefore,  in  fairness  both  to  buyer 
and  seller  we  must  measure  (weigh),  i.e.  find  out  the 
exact  quantity  of  butter  and  of  money. 

TEACHER.  Now,  let  us  suppose  that  I  am  a  buyer. 
I  wish  to  buy  some  eggs,  and  John  Smith  (one  of 
the  pupils)  has  this  basket  of  eggs  to  sell  (teacher 
hands  John  Smith  a  basket  containing  say  a  dozen 
blocks,  representing  eggs).  I  look  at  the  eggs  and 
I  see  that  they  are  nice  eggs,  and  I  wish  to  have 
them.  What  must  I  do  ? 

PUPIL.    You  will  ask  the  price  of  them. 

TEACHER.  Well,  John,  what  are  you  asking  for 
your  eggs  ? 

JOHN.    16  ^  a  dozen. 

TEACHER.    What  shall  I  do  now  ? 

PUPIL.  If  you  think  that  is  a  reasonable  price, 
you  will  buy  them. 

TEACHER.  Is  it  right  for  John  to  ask  me  anything 
for  them  ?  Why  ? 

PUPIL.  Yes.  Because  John  had  to  buy  the  hens, 
pay  for  their  feed,  take  care  of  them,  collect  the 
eggs,  etc. 

TEACHER.  Well  then,  is  it  right  for  me  to  be  so 
careful  about  getting  nice  eggs,  and  at  the  same 
time  cheap  ones,  when  John  has  been  put  to  so  much 
expense  and  trouble  ?  Why  ? 


SUGGESTIVE  LESSONS  li 

PUPIL.  Yes.  Because  you  had  to  work  hard  for 
your  money,  and  if  you  were  not  careful  with  it,  you 
would  not  have  enough  for  all  your  needs. 

TEACHER.  Well,  John,  as  long  as  it  is  a  fair  bar- 
gain, here  is  your  money  for  the  eggs.  (Teacher 
lays  a  pile  of  pennies  on  John's  desk  and  takes  the 
eggs.) 

JOHN.  Very  well,  there  is  just  one  dozen  in  the 
basket. 

TEACHER.  Will  John  at  once  put  the  money  in 
his  pocket,  and  will  I  take  the  eggs  off  home  ? 

PUPIL.  No  ;  I  think  John  will  see  if  you  gave  him 
enough  money,  and  you  will  see  if  you  have  exactly 
a  dozen  eggs. 

TEACHER.  Is  this  done  because  John  may  think 
I  am  dishonest,  or  wish  to  cheat  him  if  I  could,  and 
because  I  think  John  is  dishonest  ? 

PUPIL.  No ;  but  because  people  sometimes  make 
mistakes  unintentionally. 

TEACHER.  Well,  let  us  consider  this  pile  of 
John's  money  first,  and  see  how  John  is  going  to 
find  out  whether  he  has  the  right  money  or  not. 
What  is  all  he  knows  about  it  as  it  stands  ? 

PUPIL.    He  knows  that  it  is  a  pile  of  coins  ? 

TEACHER.  Does  he  or  do  any  of  you  know  exactly 
how  many  there  are  ? 

PUPIL.    No. 

TEACHER.    How  shall  we  find  out  ? 

PUPIL.    Count  the  pennies. 


Hi  SUGGESTIVE   LESSONS 

TEACHER.  Can  we  count  them  just  as  they  lie  in 
a  pile  ? 

PUPIL.    No. 

TEACHER.    What  must  be  done  with  them  ? 

PUPIL.    They  must  be  separated  into  parts. 

TEACHER.  (Separates  them.)  They  are  separated 
now.  (If  pupils  can  count  bjr  twos,  fours,  etc.,  they 
may  be  separated  in  different  ways.)  How  many 
parts  are  there  ? 

PUPIL.  We  cannot  tell  except  by  counting  the 
number  of  parts. 

TEACHER.  All  of  you  see  if  John  counts  them 
right.  How  many,  John  ? 

.JOHN.  Eight  parts  of  2  cents  each  (or  16  parts  of 
1^  each,  4  parts  of  4^  each,  as  the  case  may  be),  or 
16  cents. 

TEACHER.  Then,  I  made  no  mistake.  Now,  about 
my  eggs  ;  do  any  of  you  know  for  sure  how  many 
eggs  there  are  in  this  basket  ? 

PUPIL.   No. 

TEACHER.    How  can  I  make  sure  ? 

PUPIL.  By  separating  into  parts  and  counting 
the  parts. 

TEACHER.  Do  so  for  me  (one  pupil  is  asked  to 
find  out) .  How  many  ? 

PUPIL.    Six  twos  or  12  eggs. 

TEACHER.  Into  what  size  parts  was  the  basket 
of  eggs  divided  ? 

PUPIL.    Twos. 


SUGGESTIVE  LESSONS  liii 

TEACHER.    What  was  the  number  of  twos  ? 

PtiPiL.    Six. 

TEACHER.  Let  us  go  back  a  little  ,  in  the  case 
of  the  eggs  and  the  money,  what  did  we  start  with  ? 

PUPIL.  A  pile  (quantity)  of  money  in  one  case 
and  a  pile  (or  quantity)  of  eggs  in  the  other. 

TEACHER.    What  did  we  want  to  find  ? 

PUPIL.    The  exact  value  or  size  of  the  pile. 

TEACHER.    How  did  we  do  this  ? 

PUPIL.  By  separating  into  known  parts  and  find- 
ing the  number  of  parts. 

TEACHER.  Couldn't  we  have  found  out  without 
separating  into  parts  of  some  kind  ? 

PUPIL.    No. 

TEACHER.  Well,  after  we  had  separated  into  parts 
(ones,  or  twos,  or  threes),  could  we  not  tell,  without 
finding  out  the  number  of  parts  ? 

PUPIL.    No. 

TEACHER.  Let  us  now  see  if  we  do  the  same  in 
all  cases.  Suppose  this  stick  that  I  have  is  a  mould- 
ing I  bought  for  framing  a  small  picture,  and  I  wish 
to  know  how  much  moulding  I  have  ;  can  any  of 
you  tell  me  exactly  ? 

PUPIL.  No ;  but  1  think  I  could  guess  pretty  near 
it. 

TEACHER.  Yes ;  but  mere  guessing  would  not  be 
fair  either  to  buyer  or  seller  ;  we  found  that  out  in 
the  case  of  butter  and  eggs.  How  can  I  find  out 
exactly  ? 


liv  SUGGESTIVE   LESSONS 

PUPIL.    By  measuring  it. 

TEACHER.    What  shall  I  use  to  measure  it  ? 

PUPIL.  One-inch,  two-inch,  six-inch,  foot,  or  any 
length-measure  you  wish. 

TEACHER.  Well,  it  would  take  too  long  with  a 
1-inch  measure ;  we  shall  use  the  6-inch.  How  am 
I  to  measure  it,  now  that  I  have  chosen  what  to 
measure  with  ? 

PUPIL.  Apply  the  6-inch  measure,  and  mark  off 
as  many  as  there  are. 

TEACHER.  Well,  Frank,  you  do  so  for  me.  What 
have  we  done  so  far  ? 

PUPIL.    We  have  separated  it  into  parts. 

TEACHER.  Do  we  know  the  measure  of  the  mould- 
ing yet  ?  What  is  to  be  done  yet  ? 

PUPIL.  No,  the  number  of  parts  must  be  found  by 
counting.  There  are  six  6-inch  parts,  or  the  mould- 
ing is  3  feet  long. 

TEACHER.  Now  tell  me  what  we  started  with  in 
the  case  of  the  moulding  and  the  successive  steps  we 
went  through  ? 

PUPIL.  We  started  with  an  unknown  length  or 
quantity,  divided  it  into  parts,  and  found  the  num- 
ber of  the  parts. 

TEACHER.  Did  we  do  exactly  the  same  thing  as 
in  each  of  the  other  cases  ? 

PUPIL.    Yes. 

TEACHER.  Similarly,  if  we  wish  to  find  the  num- 
ber of  cords  in  a  pile  of  wood,  or  the  number  of 


SUGGESTIVE   LESSONS  lv 

cattle  in  a  field;  in  fact,  if  we  wish  to  get  a  right 
idea  of  any  quantity,  what  do  we  always  start  with  ? 

PUPIL.  We  always  start  with  the  quantity  and 
try  to  get  an  exact  idea  of  it. 

TEACHER.    In  order  to  do  this  what  must  be  done  ? 

PUPIL.  We  must  choose  some  part  or  measure  by 
which  to  measure  the  whole,  and  break  up  the  whole 
into  as  many  of  these  parts  as  it  contains. 

TEACHER.  What  still  remains  to  be  done  before 
the  quantity  becomes  known  definitely  ? 

PUPIL.  The  number  of  parts  must  be  found  by 
counting. 

TEACHER.  I  may  now  tell  you  that  the  part  we 
have  used  in  each  case  to  measure  (to  get  a  correct 
idea  of)  the  whole  is  called  the  unit  of  measure. 
What  unit  of  measure  might  we  use  to  measure  a 
pail  of  milk  ?  A  quantity  of  potatoes  ?  etc.  . 

PUPIL.    Pint,  2-pint,  or  quart.     Peck,  bushel,  etc. 

TEACHER.  But  even  after  we  had  separated  the 
whole  into  minor  parts  by  use  of  the  unit  of  measure, 
what  in  each  case  had  to  be  done  before  we  knew  the 
exact  measurement  of  the  quantity  we  desired  to 
measure  ? 

PUPIL.    We  had  to  find  the  number  of  parts. 

TEACHER.  Well,  then,  what  might  we  say  num- 
ber is  ? 

PUPIL.  It  is  that  which  tells  us  how  many  parts 
or  "  units  "  make  up  the  whole  quantity. 

TEACHER.    Could  we  find  exactly  hoiv  much  a 


Ivi  SUGGESTIVE   LESSONS 

quantity  is  without  finding  how  many  units  (parts) 
make  it  up  ? 

PUPIL.    No. 

TEACHER.    What  do  we  call  this  how  many  ? 

PUPIL.    Number. 

TEACHER.  For  that  reason  we  say  briefly  that 
number  is  the  instrument  we  use  in  order  to  measure 
quantities  or  is  "the  tool  of  measurement." 


IX.  Multiplication. 

A  LESSON  LEADING  TO  THE  MULTIPLICATION 
TABLE. 

TEACHER.  Count  the  number  of  hands  there  are 
in  this  class. 

PUPIL.    1,  2,  3,  4,  5,  6,  7,  8,  9,  10,  11,  12. 

TEACHER.    Find  out  by  adding  by  twos. 

PUPIL.  Two  and  two  are  four;  four  and  two  are 
six,  etc. 

TEACHER.  It  may  be  done  more  quickly  still  by 
counting  by  twos. 

PUPIL.    Two,  four,  six,  etc. 

TEACHER.  Count  the  pupils  by  twos,  and  tell  me 
how  many  times  there  are  two  hands  in  the  class. 

PUPIL.    Two,  four,  six.     Six  times  two  hands. 

TEACHER.  I  am  going  to  make  a  large  square  of 
these  small  squares,  and  I  want  you  to  tell  me  how 
many  small  ones  there  are.  How  many  in  each  row  ? 


SUGGESTIVE   LESSONS  Ivii 

PUPIL.    Nine  squares.     Three  in  each  row. 

TEACHER.    Count  them  by  thre 

PUPIL.    Three,  six,  nine. 

TEACHER.  How  many  times  have  we  three  small 
squares  to  make  one  large  square  ? 

PUPIL.    Three  times. 

TEACHER.  Here  is  a  cardboard  oblong  and  a 
2-inch  measure  for  each  of  you.  I  want  you  to 
mark  off  the  length  and  width  in  units  of  2  inches, 
and  find  how  many  times  the  unit  is  repeated  for 
each. 

PUPIL.    Length,  5  times  2  inches;  width,  3  times 

2  inches. 

TEACHER.  Add  up  the  length  and  width,  and  find 
out  the  dimensions  of  the  oblong. 

PUPIL.    Length,  10  inches ;  width,  6  inches. 

TEACHER.  Then  what  is  5  times  2  inches?  What 
is  6  inches  equal  to  ? 

PUPIL.    5  times  2  inches  =  10  inches ;  6  inches  = 

3  times  2  inches. 

TEACHER.  With  these  blocks  I  want  you  all  to 
lay  two  rows  of  blocks  from  one  end  of  your  slate  to 
the  other,  and  then  tell  me  how  many  twos  you  had 
to  place  to  do  so. 

PUPIL.    Eight  twos. 

TEACHER.  Now  find  out  how  much  eight  times 
two  is. 

PUPIL.    Eight  times  two  blocks  is  16  blocks. 

TEACHER.    Now  here  is  a  stick  16  inches  long. 


Iviii  SUGGESTIVE   LESSONS 

What  unit  shall  we  use  to  find  how  many  2-inches  in 
the  length  of  it  ? 

PUPIL.    Two-inch  measure. 

TEACHER.  Now  measure  it. and  tell  me  how  many 
times  2  inches  make  16  inches. 

PUPIL.    Eight  times  2  inches  make  16  inches. 

TEACHER.    How  much  would  8  times  2  blocks  be  ? 

PUPIL.    Eight  times  2  blocks  is  16  blocks. 

TEACHER.  Eight  times  $2?  2  apples?  2  any- 
thing ? 

PUPIL.    Sixteen. 

TEACHER.  You  found  out  what  3  times  2  inches 
makes;  what  would  3  times  12  make ?  3  times  2  lb.? 
3  times  2  anything? 

PUPIL.    Six  dollars,  six  pounds,  etc. 

TEACHER.  Here  are  some  additions  I  would  like 
you  all  to  do.  What  shall  we  say  each  2  stands  for 
to-day  ? 

f2     2     2     2 
2222 


PUPIL.    Pounds. 


222  etc. 


(to  twelve 
twos). 


2     2 
2 

TEACHER.    Now  I  would  like  to  know  your  an- 
swers. 

PUPIL.    4,  6,  8,  10,  etc;,  pounds. 
TEACHER.    What  do  we  call  the  numbers  we  add  ? 
PUPIL.    Addends. 

TEACHER:    Can  you   tell   me    anything   peculiar 
about  the  addends  in  these  questions? 


SUGGESTIVE  LESSONS  Hx 

PUPIL.    They  are  all  twos. 

TEACHER.    How  many  twos  in  the  first,  second, 
third,  etc.,  questions? 

PUPIL.    2,  3,  4,  etc.,  twos. 

TEACHER.    When  you  were  adding  the  twos  did 
you  think  of  how  many  addends  there  were  ? 

PUPIL.    No. 

TEACHER.    What  made  4  in  the  first  question  ? 

PUPIL.    Two  and  two. 

TEACHER.    But  tell  me  the  same  thing  in  another 
way. 

PUPIL.    Two  times  two. 

TEACHER.    Now  what  do  you  learn  from  second 
question?  third?  etc. 

PUPIL.    Three   times   2   Ib.  make  6  Ib.,  4  times 
2  Ib.  make  8  Ib.,  etc. 

TEACHER.    How  did  you  get  the  numbers  3,  4, 
etc.? 

PUPIL.    By  counting  the  addends. 

TEACHER.    Did  you  do  that  when  adding  ? 

PUPIL.    No. 

TEACHER.    Then  you  see  we  have  started  some- 
thing different  from  adding. 

Now  write  out  on  your  slates  what  we  learn  from 
each  of  the  above  questions. 

2  times  2  makes  4, 

p  3  times  2- makes  6, 

4  times  2  makes  8, 
etc. 


lx  SUGGESTIVE    LESSONS 

TEACHER.  How  many  times  did  you  write  the 
words  "  times  "  and  "  makes  "  ? 

PUPIL.    Eleven. 

TEACHER.  Now  I  will  show  you  a  shorter  way  of 
writing  it,  as  that  takes  too  long.  For  "  times  "  we 
use  the  sign  "  x  ",  and  for  "makes"  the  sign  "  =  ," 
which  means  equals.  Then  we  have 

2x2  =  4, 

3x2  =  6, 

4x2  =  8, 

etc. 

TEACHER.  This  is  what  we  call  the  multiplication 
table  for  two  times,  and  I  would  like  you  all  to  learn 
it  for  me,  because  you  see  how  handy  it  is  to  say  that 
8  times  2  anything  is  16,  instead  of  adding  up  8  twos. 
I  will  show  you  how  handy  it  is.  We  will  build  up 
an  oblong  block  of  small  cubic  inch  blocks,  and  I 
would  like  you  to  find  out,  when  it  is  built,  how  many 
small  blocks  we  have  used,  without  counting  or  add- 
ing. (Size  5"  high,  2"  wide,  2"  thick.)  How  will 
you  do  it  ? 

PUPIL.    By  finding  how  many  twos  in  it, 

TEACHER.    How  many  layers  have  we  ? 

PUPIL.    Five. 

TEACHER.    How  many  in  each  layer  ? 

PUPIL.    Four. 

TEACHER.    Yes  ;  but  how  many  twos  is  that  ? 

PUPIL.    Two  twos. 


SUGGESTIVE  LESSONS  Ixi 

TEACHER.    Well,  how  many  two-twos   shall  we 
have  in  five  layers? 
PUPIL.    Five  two-twos. 

TEACHER.    How  many  twos  will  that  make  ? 
PUPIL.    Ten  twos. 
TEACHER.    Now,  what  is  ten  twos  ? 
PUPIL.    Twenty  blocks,  20  cu.  in. 

X.  Reduction 

The  following  lesson  is  suggested  to  precede  Les- 
son 23,  questions  1,  2,  7,  8.  Establish  in  the  mind 
of  the  children  the  relation  between  the  pint  and 
the  quart  by  actual  measurement.  Let  the  teacher 
measure  3  qt.  of  water  into  a  pail  without  the  class 
knowing  how  much  is  put  in.  Ask  the  class  indi- 
vidually to  state  how  much  water  is  in  the  pail. 
Answers  will  vary,  thus  showing  the  necessity  for 
accurately  measuring  the  quantity.  Pupils  will  sug- 
gest the  quart  as  the  unit  of  measure.  On  counting, 
as  the  water  is  measured,  they  will  get  the  number 
3 ;  i.e.  there  were  3  qt.  in  the  pail.  Write  on  the 
board  3  qt. 

What  number  will  you  get  if  you  measure  with 
a  pint?  Measure;  the  pupils  count  6,  i.e.  6  pt. 
Write  on  the  board  3  qt.  =  6  pt.  In  the  same  way, 
without  the  class  knowing  how  much  water  is  put 
in  the  pail,  measure  2  qt.,  4  qt.,  etc.  Let  the  class 
count  the  corresponding  numbers  and  derive  2  qt.  = 
4  pt.,  4  qt.  =8  pt.,  and  so  on. 


Ixii  SUGGESTIVE  LESSONS 

This  by  actual  measurement.     Now  express  these 
relations  without  actual  measurement. 

5  qt.  =  ?  pt.       6  qt.  =  ?  pt.       8  qt.  =  ?  pt. 
?  qt.  =  4  pt.       ?  qt.  =  6  pt.       ?  qt.  =  10  pt. 
and  so  on. 


Again : 

If  each  dot  represents  1  pt.,  what  will  2  dots 
represent  (1  qt.)? 

Count  by  pints  (1,  2,  3,  4,  5,  6).  Count  by  quarts 
(1,  2,  3).  6pt.=  3  qt. 


If  these  dots  represent  the  quantity  of  water  in 
the  pail,  each  dot  representing  1  pt.,  how  much  water 
is  in  the  pail?  (4  qt.)  How  many  pints?  (8  pt.) 
4  qt.  =  8  pt. 


If  these  dots  represent  the  quantity  of  water  in  a 
pail,  how  many  pints  are  in  the  pail?  (10.)  How 
many  quarts?  (5.)  10  pt.  =  5  qt.  And  so  on. 

Ask  pupils  to  represent  on  the  board  the  water  in 
a  pail  containing,  say,  4  qt. 
-  What  other  measurement  is  indicated?     (8  pt.) 

What  is  assumed  about  the  dots  ? 

Do  the  same  kind  of  work,  putting  into  the  pail 
3  qt.  1  pt.,  2  qt.  1  pt.,  4  qt.  1  pt.,  and  so  on.  Use 


SUGGESTIVE  LESSONS  Ixiii 

the  dots  to  give  facility  in  operation  as  soon  as  the 
actual  measurement  has  been  done. 

It  will  be  seen  that  in  the  above  work  the  children 
start  with  a  whole  unmeasured  quantity  which  they 
have  a  motive  for  measuring. 

In  order  to  measure  the  quantity,  they  select  a 
unit,  and  while  measuring  count  the  number  which 
arises  out  of  the  measurement.  The  unit  and  the 
number  together  (3  qt.)  measure  the  quantity,  which 
is  now  definitely  known.  A  second  measurement 
with  a  different  unit  gives  rise,  in  a  similar  way, 
to  6  pt.,  and  establishes  the  relation  3  qt.  =  6  pt. 
After  the  process  is  once  understood  by  actual 
measurement,  the  symbolic  representation  by  means 
of  dots  enforces  and  gives  facility  in  the  operations. 
Similarly,  for  the  more  complex  reductions,  3  qt.  1  pt. 
=  7  pt.  and  7  pt.  =  3  qt.  1  pt. 


SUGGESTIONS 


Lessons  1-8 

"  Suggestions  to  Teachers,"  Sections  I. -IV.,  have 
special  reference  to  these  lessons. 

Lesson  9 

From  the  preceding  work  the  children  know  that 
2  and  3  are  5.  Draw  a  line  15  in.  long  and  measure 
one  part  12  in.  long.  How  long  is  the  other  part  ? 
Test  the  answers  by  measuring. 

Draw  a  line  25  in.  long  and  measure  one  part  3  in. 
long.  How  long  is  the  other  part  ?  Measure. 

Similarly  draw  and  divide  a  line  35  in.  long.  A 
yard  stick  divided  into  inches  can  be  used  for  meas- 
uring. Express  the  results  orally  and  in  writing  on 
the  board.  Give  many  practical  questions  such  as 
question  2. 

In  question  3  let  the  class  note  where  the  5-min. 
mark  is.  Turn  the  hand  through  2  minute  spaces. 
How  many  more  to  reach  the  5-min.  mark  ?  Simi- 
larly for  15  min.  Turn  the  hand  through  3  minute 
spaces.  How  many  more  ?  Similarly  for  25  min. 

Ixiv 


SUGGESTIONS 

Turn  through  22  minute  spaces.  How  many  more  ? 
Continue  this  work  until  the  sum  equals  55  min., 
constantly  giving  the  children  the  opportunity  to 
make  inferences. 

The  children  will  then  infer  that 

62  +  3  =  65.     72  +  3  =  75. 

This  work  at  the  board  should  precede  Lesson  1, 
and,  in  fact,  all  or  nearly  all  of  the  succeeding 
lessons  should  be  preceded  by  oral  work  on  the  part 
of  the  teacher  with  the  class.  Teach  and  use  con- 
tractions from  the  first,  and  constantly  intersperse 
the  work  with  simple  practical  questions  such  as 
questions  2,  4,  7,  13. 

In  adding  and  subtracting  use  many  different  units 
as  in  questions  16,  17,  and  18. 

Lesson  10 

Introduce  this  lesson  by  actual  measurement  as  in 
Lesson  9.  In  question  13  let  it  be  understood  that 
each  dot  represents  some  unit  of  measure  as  1  in., 
1^,  2  lb.,  3  yd.,  and  repeat  the  question,  using  differ- 
ent units.  Thus,  5  3-yd.  =  4  3-yd,  +  1  3-yd.,  and 
so  on. 

In  question  15  let  the  class  discover  that  there 
are  only  four  combinations  that  give  5. 

Gradually  develop  the  idea  that  the  unit  and  the 
number  together  measure  quantity.  Thus,  let  the 
teacher  draw  on  the  board  a  line  without  the  pupils 


SUGGESTIONS 

knowing  how  long  it  is.  Ask  the  pupils  to  judge 
of  its  length.  Answers  will  vary,  showing  the  need 
of  a  definite  method  of  measurement.  Measure 
with  a  foot  measure.  How  many  times  did  you 
measure?  (4.)  Thus  the  pupils  had  an  unknown 
quantity  to  be  measured  and  a  unit  of  measure.  In 
process  of  measurement  they  got  by  counting  the 
number  4.  Thus  the  quantity,  which  is  now  known 
to  be  4  ft.,  is  definitely  measured  in  terms  of  the 
number  4  and  the  unit  1  ft.  Other  quantities  and 
units  may  be  chosen.  See  "  Suggestions  to  Teachers," 
L,  §§12  and  13. 

Lesson  11 

Questions  1,  2,  3,  10,  are  a  preparation  for  sub- 
traction. The  pupils  have  already  learned  that  2 
and  3  are  5  (Addition),  which  carries  with  it  the 
idea  that  2  and  3  are  5  (Subtraction).  In  oral  drill 
put  the  questions  also  in  the  form  of  Lesson  1 2,  ques- 
tion 19.  See  "  Public  School  Arithmetic,"  §§  42,  44. 

In  such  questions  as  12,  13,  let  the  teacher  place 
the  points  without  the  pupils  knowing  how  far  they 
are  apart.  Measure  first  with  a  yardstick,  and 
again  with  a  foot  rule.  In  question  17  apply  the 
same  principle  to  the  water  put  into  the  pail.  As 
soon  as  it  can  be  done  intelligently  suggest  the  more 
economical  way  of  reducing  without  actually  measur- 
ing. The  placing  of  dots  as  in  question  18  will 
assist  in  this.  See  "  Suggestions,"  X.  Reduction. 


SUGGESTIONS  Ixvii 

Lesson  14 

Before  this  lesson  is  studied  let  the  pupils  measure 
different  lengths,  as  the  length  of  the  table,  and 
express  their  results  thus,  1  yd.  2  ft.  6  in.  Have 
the  children  read  these  results.  This  will  show  the 
necessity  of  the  three  units  of  length.  Having  done 
this,  measure  such  lengths  as  are  given  in  the  lesson; 
add,  and  verify  results  by  actual  measurement. 

Make  such  simple  practical  questions  as  13—21. 

Lesson  15 

In  this  lesson  and  also  in  subsequent  lessons,  when 
necessary,  use  the  foot  ruler  or  clock  face,  and 
illustrate  the  additions  as  in  Lesson  1. 

Give  many  questions  in  subtraction,  here  and  else- 
where, complementary  to  such  questions  as  2,  3,  4,  6, 
8,  9,  etc. 

Thus: 

Subtract:  *7  *17  26  27  62626 
4  14  24  3  2  21  4 

Lesson  17 

Read  question  1,  not  2  +  2  =  4,  4  +  2  =  6,  but  2, 
4,  6  ;  1,  3,  6,  etc. 

In  adding  such  questions  as  2,  the  lowest  number 
or  12  (see  footnote,  page  40)  had  better  be  omitted 
after  a  little  practice,  the  pupil  simply  saying  14, 16. 

*  Read  4  +  3  =  7;    14  +  3  =  17. 


Ixviii  SUGGESTIONS 

In  adding  21  /  to  13  £  think  of  the  2  in  21^  as  2 
dimes,  and  the  1  in  13^  as  1  dime. 

Lesson  18 

In  the  operations  in  questions  7,  8,  and  9,  let  the 
pupil  fancy  that  he  is  doing  addition  with  the  sum 
at  the  top,  and  as  he  works  set  down  the  figures 
3  and  1. 

Lesson  19 

Use  such  questions  as  16,  17,  18,  gradually  to 
develop  the  idea.  (1)  that  the  quantity  is  found  by 
multiplying  the  unit  by  the  number,  (2)  that  the 
number  is  found  by  dividing  the  quantity  by  the  unit, 
(3)  that  the  unit  is  found  by  dividing  the  quantity 
by  the  number. 

Lesson  30 

Note  that  in  question  1  the  sums  are  found  by 
addition.  In  question  2  we  find  that  the  $  2  in  the 
last  column  is  repeated  6  times. 

Thus  we  think  of  the  unit  $2  and  the  number  6, 
giving  as  their  product  $  12. 

For  this  change  from  addition  to  multiplication 
see  the  "Public  School  Arithmetic,"  §  47. 

Read  the  sign  x  as  times,  thus  3  x  $  2  =  3  times 

Use  the  dots  to  develop  the  law  of  commutation, 
viz.  :  2x3  =  3x2;  4x6  =  6x4,  etc. 


SUGGESTIONS  Ixix 

Lesson  31 

Develop  some  parts  of  the  multiplication  tables  by 
actual  measurement  with  units  of  different  lengths. 
Thus,  cut  out  of  cardboard  12  units  of  lengths, 
respectively,  1  in.,  2  in.,  3  in.,  •••  12  in.  long.  Draw 
a  line  on  the  board  and  measure  along  this  line  with 
each  unit,  twice.  Then,  with  a  yardstick,  measure 
results,  and  we  have  the  table  of  2.  Or,  again, 
repeat  the  unit  2  in.  from  1  to  12  times,  write  the 
corresponding  results,  and  by  the  law  of  commuta- 
tion we  have  the  table  of  2. 

Extend  the  table  as  in  questions  3,  4,  7,  8,  9. 

Have  the  class  make  simple  practical  examples, 
founding  them  on  questions  11  and  12,  or  give  them 
such  a  price  list  as  is  found  on  page  75,  question  23. 

Lesson  33 

Bring  out  the  fact  that  in  measuring  distance  we 
have  the  units  1  in.,  1  ft.,  1  yd.,  and  1  mi.  We 
measure  the  value  of  things  with  the  units  1^  and 
•$1.  We  measure  milk  with  the  unit  1  qt.,  kerosene 
Avith  the  unit  1  gal.,  and  so  on.  Hence  to  measure 
area  (a  different  kind  of  quantity),  we  need  a  new 
unit,  and  this  we  naturally  derive  from  the  unit 
1  in.  Give  plenty  of  work  to  precede  this  lesson, 
and  let  the  children  draw  and  cut  out  and  divide 
simple  areas. 

Teach  the  area  of  an  oblong  somewhat  after  this 
fashion.  Have  the  pupils  draw  oblongs,  say  4  in. 


Ixx  SUGGESTIONS 

by  3  in.  Divide  them  into  square  inches.  Count 
the  number  of  square  inches.  Count  again  by 
4  sq.  in.  How  many  (3  4  sq.  in.  or  12  sq.  in.)? 
Count  again  by  3  sq.  in.  How  many  (4  3  sq.  in.  or 
12  sq.  in.)?  Which  of  the  three  methods  is  most 
economical?  (Either  of  the  last  two,  i.e.  find  tha 
area  by  multiplication,  not  by  addition.)  What 
would  be  the  area  if  the  oblong  were  5  in.  long 
and  3  wide  ?  6  in.  long  ?  8  in.  long  ?  5  in.  long 
and  4  in.  wide,  and  so  on  ?  Use  other  units  of  length 
(2  in.,  3  in.,  1  ft.,  1  yd.,  1  mi.). 

Lesson  34 

The  purpose  of  this  lesson  is  to  prepare  the  way 
for  division.  Just  as  the  preceding  work  in  addition 
and  subtraction  has  made  of  the  two  substantially 
one  process,  so  the  child  should  be  led  to  think  of 
multiplication  and  division  as  substantially  one  pro- 
cess. In  multiplication  4  and  2  are  factors  of  ? 
In  division  4  and  ?  are  factors  of  8. 

See  "  Public  School  Arithmetic,"  preface,  §  2,  and 
also  §§  60-63. 

Lesson  35 

Write  the  multiplication  table  of  2  on  the  board 
in  a  column,  thus  : 

2  x    1  in.  =    2  in. 
2  x    2  in.  =    4  in. 


2  x  12  in.  =  24  in. 


SUGGESTIONS  lxxi 

Drill  thus  : 

l  of  2  in.  =  ?  1  of  4  in.  =  ?  J  of  6  in.  =  ?  and 
so  on  in  any  order.  Also  J  of  20  in.  =  ?  \  of 
200  in.  =  ?  and  so  on.  Illustrate,  if  necessary,  by 
drawing  lines  4  in.,  6  in.,  8  in.,  etc.,  and  dividing 
them  into  two  equal  parts. 

Similarly,  drill  thus  : 

4  in.  -5-  2  in.  =  ?  6  in.  -s-  3  in.  =  ?  8  in.  -=-  4  in.  ='? 
and  so  on  in  any  order.  Also  40  in.  -v-  2  in.  =  ? 
80  in.  -j-  4  in.  =  ?  80  in.  -r-  40  in.  =  ?  and  so  on. 
Illustrate,  if  necessary,  by  cutting  from  cardboard 
strips  2  in.,  3  in.,  4  in.,  5  in.,  etc.,  and  using  these 
lines  as  units  to  measure  the  lines  respectively  4  in., 
6  in.,  8  in.,  etc.  Drill  until  this  is  mastered  in  any 
order.  Use  other  units  instead  of  1  in.,  as  $1,  1^, 
1  lb.,  1  qt.,  etc.  Throughout  this  work  give  many 
practical  examples.  (See  Lesson  34,  questions 
8-14.)  Give  also  such  examples  as  the  following  : 
16  pt.  -r-  2  pt.  =  ?  How  many  quarts  in  16  pt.  ? 

8  qt.  -r-    4  qt.  =  ?     How  many  gallons  in  8  qt.  ? 
16  qt.  -f-    8  qt.  =  ?     How  many  pecks  in  16  qt.  ? 

8  pk.  -f-    4  pk.  =  ?     How  many  bushels  in  8  pk.  ? 
24  in.   -j- 12  in.    =  ?     How  many  feet  in  24  in.  ? 

-|-  of  4  pt.  =  ?  What  unit  of  measure  ?  \  of  8  qt.  =  ? 
What  unit  ?  J  of  16  qt.  =  ?  What  unit  ?  \  of 
8  pk.  =  ?  What  unit  ?  J  of  24  in.  =  ?  What  unit  ? 

Name  the  odd  numbers  from  1  to  25.  .What  num- 
ber must  be  subtracted  from  these  odd  numbers  to 
make  them  exactly  divisible  by  2  ? 


SUGGESTIONS 

It  is  expected  that  with  the  price  list  furnished  ir. 
question  23,  the  pupils  will  make  examples  similar 
to  questions  14,  21,  22. 

Lesson  36 

Correlate  the  work  in  ratio  with  counting  and 
measurement.  For  instance,  measure  a  12-in.  line 
with  a  2-in.  unit,  a  3-in.  unit,  a  4-in.  unit,  a  6-in. 
unit.  Count  the  number  of  measurements  each 
time.  6  is  often  called  the  ratio  of  12  in.  to  2  in., 
4  that  of  12  in.  to  3  in.,  3  that  of  12  in.  to  4  in., 
and  2  that  of  12  in.  to  6  in.  Again  what  part  of 
12  in.  is  equal  to  6  in.  ?  (J)  ^  is  often  called  the 
ratio  of  6  in.  to  12  in.,  and  so  on. 

After  the  children  have  noted  by  drawings  the 
simple  instances  given  in  the  lessons,  write  the  mul- 
tiplication table  of  2  on  the  board,  thus  : 

2  times 


4*" 

12  ^" 

Then  note  from  this  table  what  2  is  the  ratio  of 
and  what  J  is  the  ratio  of.  Give  such  examples  as 
J-  is  the  ratio  of  4^  to  ?  6^  to  ?  Of  ?  to  12*.  Of? 
to!8£  Of  11^  to? 


SUGGKSTiONS  Ixxiii 

Give  similar  examples  with  2  as  the  ratio.  Use 
other  units.  Give  easy  concrete  examples  similar 
to  the  questions  in  Lesson  40. 

Lesson  38 

See  suggestions,  Lesson  36. 

Lesson  39 

Do  as  much  actual  measurement  as  is  necessary  to 
illustrate  this  lesson.  Measure  the  length  and  width 
of  the  room,  of  tables,  desks,  books,  height  of  pupils, 
and  so  on.  Note  the  size  of  books  as  measured 
by  the  number  of  pages.  Measure  the  quantity  of 
water  in  a  pail  or  pitcher,  the  unit  being  1  pt.  or 
1  qt.  or  1  gal.  Weigh  different  articles,  and  find 
the  weight  of  different  pupils.  Make  it  clear  that  in 
order  to  measure  any  quantity  we  must  use  a  suitable 
unit  of  measure  and  we  must  find  the  number  of  units 
that  measures  the  quantity. 

Lesson  42 

Be  sure  that  the  pupils  know  by  actual  measure- 
ment that  1  gal.  =  4  qt.,  and  similarly  with  other 
tables  referred  to  in  this  book. 

Lesson  43 

Make  the  method  of  finding  the  area  of  an  oblong 
clear  by  drawings  on  paper  and  on  the  board. 
Emphasize  the  fact  that  the  area  is  measured  by 


Ixxiv  SUGGESTIONS 

the  number  and  the  unit.  Develop  the  fact  that  the 
number  measuring  the  area  is  the  product  of  the 
numbers  measuring  the  sides.  Then  use  this  fact 
to  find  the  measure  of  the  areas  and  the  areas  of  the 
oblongs.  Measure  the  dimensions  of  oblongs  in  the 
room  and  calculate  their  areas.  Let  this  work  as 
usual  precede  the  study  of  the  lesson  by  the  children. 

Lesson  45 

See  suggestions,  Lesson  35.     Use  the  table  of  3. 

Lesson  47 

Let  the  oral  work  preceding  this  lesson  be  objec- 
tive until  it  is  clearly  understood.  In  question  3, 
for  instance,  draw  lines  1 J  ft.  and  2  ft.  long.  Meas- 
ure with  a  -J  ft.  unit,  when  the  number  of  measure- 
ments will  be  respectively  3  and  4,  hence  1|  ft.  =  f  ft. 
and  2  ft.  =  J  ft.  How  can  you  reduce  2£  ft.  to  half 
feet  without  actually  measuring  ?  Similarly,  in  ques- 
tions 4  and  5,  measure  if  necessary.  In  question  8, 
take  a  string  6  in.  long,  cut  off  one  part  4%  in.  long. 
How  long  is  the  remainder  ?  Hence,  4^  in.  +  1^  in. 
=  6  in.  Similarly  with  other  parts  of  this  question. 

Lesson  48 

In  such  questions  as  16  let  it  be  clearly  under- 
stood, not  that  4  is  contained  in  16  4  times,  but  that 
4  is  contained  in  16  tens  4  tens.  Drill  on  such  ques- 
tions as  18  until  the  pupil  can  readily  see  in  any 


SUGGESTIONS 

number  the  next  smaller  number  of  which  4  is  a 
factor  and  can  give  the  remainder.  Such  measure- 
ments as  are  indicated  in  question  19  will  give  mean- 
ing to  the  process.  Let  the  pupils  state  simple 
practical  questions  corresponding  to  20  and  21. 

Lesson  49 

Practise  reduction  at  first  by  actual  measurement. 
Where  this  is  done  it  is  better  that  the  teacher  or 
some  pupil  should  fix  on  some  quantity  without  the 
class  knowing  what  it  is.  Measure  this  quantity 
with  two  or  more  units,  and  let  the  result  be,  say, 

2  ft.  4  in.     Measure  with  the  smaller  unit,  and  the 
result  is  found  to  be  28  in.     This,  stated  as  a  relation 
of  equality,  is  2  ft.  4  in.  =  28  in.     In  this  work  the 
children  have  the  unknown  quantity,  the  unit  or  units, 
the   number,  then   the   measured   quantity,    and   the 
relation  of   equality   growing    out   of    two   separate 
measurements  with  different  units.      How  do  such 
expressions  as  2  ft.  6  in.,  3  qt.  1  pt.,  and  1  hr.  -30 
min.  arise  in  the  measuring  process  ? 

As  soon  as  this  measuring  process  gives  signifi- 
cance to  the  operation,  let  the  pupils  deduce  the  rule 
and  use  it  as  the  more  economical  method.  You 
reduce  3  gal.  2  qt.  to  quarts  by  multiplying  4  qt.  by 

3  and  adding  2  qt.  to  the  product.     Practically  it  is 
awkward  to  be  constantly  changing  the  multiplier. 
Hence,  by  the  law  of   commutation,  we  have  :    To 
reduce   gallons  and  quarts  to  quarts,  multiply  the 


SUGGESTIONS 

number  of  gallons  by  4  and  add  the  number  of 
quarts.  What  is  the  multiplier  in  reducing  yards 
to  feet? 

Lesson  50 

An  oblong  4  in.  long  and  3  in.  wide  contains  12 
;•(]_.  in.;  one  4  2-in.  long  and  3  2-in.  wide  contains 
[2  2-in.  squares  or  12  4  sq.  in.,  i.e.  48  sq.  in.  An 
o')long  10  in.  (5  2-in.)  long  and  8  in.  (4  2-in.)  wide 
contains  5x4,  or  20,  2-in.  squares  or  20  4  sq.  in., 
i.e.  80  sq.  in.  Here  the  unit  that  measures  the 
length  is  2-in.  and  that  which  measures  the  area  is 
the  2-in.  square  or  4  sq.  in. 

Lesson  52 

Teach  the  pupil  to  take  ^  of  a  quantity  by  divid- 
ing it  by  3.  This  is  much  more  economical  practi- 
cally than  for  him  to  think  of  one  operation  for 
finding  J  of  a  quantity  and  another  for  dividing 
it  by  3.  Teach  him  to  take  f  of  a  quantity  by 
dividing  it  by  3  and  multiplying  by  2,  or  by  multi- 
plying the  quantity  by  2  and  dividing  the  product 
by  3. 

Lesson  54 

See  suggestions,  Lesson  36. 

In  order  to  make  the  oral  lesson  in  ratio  apply  to 
the  solution  of  problems,  it  is  not  sufficient  merely 
to  state  the  ratio  of  the  given  quantities.  State  also 
the  ratio  of  their  cost,  for  instance.  What  is  the 


SUGGESTIONS  Ixxvii 

ratio  of  20  Ib.  to  5  Ib.  ?  Of  5  Ib.  to  20  Ib.  ?  Of 
the  cost  of  20  Ib.  of  sugar  to  that  of  5  Ib.  ?  Of  the 
cost  of  5  Ib.  of  sugar  to  that  of  20  Ib.  ?  If  5  Ib.  of 
sugar  cost  25  £  what  will  20  Ib.  cost?  If  20  Ib. 
of  sugar  cost  104^,  what  will  5  Ib.  cost? 

Again,  what  is  the  ratio  of  20  mi.  to  4  mi.  ?  Of 
the  time  a  boy  can  ride  20  mi.  to  that  which  he  will 
need  to  ride  5  mi.  ?  If  a  boy  rides  on  his  bicycle 
5  mi.  in  ^  hr.,  how  long  will  it  take  him,  at  the 
same  rate,  to  ride  20  mi.  ?  Connect  closely  the  ratio 
and  its  reciprocal.  What  is  the  ratio  of  20  mi.  to 
5  mi.  ?  What  is  the  (reciprocal)  ratio  of  5  mi. 
to  20  mi.  ?  So  also  with  practical  examples,  as 
follows  : 

(1)  If  a  man  drives  5  mi.  in  f  hr.,  how  long  will 
it  take  him,  at  the  same  rate,  to  drive  20  mi.  ? 

(2)  If  a  train  ran  20  mi.  in  36  min.,  how  long  did 
it  take  on  the  average  for  each  5  mi.  ? 

Questions  (1)  and  (2)  involve  reciprocal  ratios. 

Lesson  57 

Question  10,  etc.  Take  points  on  the  board  2  ft., 
3  ft.,  and  so  on  apart,  without  the  pupils  knowing 
the  distance.  Measure  with  the  1-ft.  unit.  Measure 
also  with  the  units  |  ft.,  J  ft.,  \  ft.,  and  deduce  the 
relations  2  ft.  =  f  ft.  =  f  ft.  =  f  ft,  ;  3  ft.  =  f  ft. 
=  f  ft.  =  Jj2-  ft.  Develop  the  rule  that  to  reduce 
a  number  of  feet  to  halves,  thirds,  or  fourths,  you 
multiply  the  number  of  feet  by  2,  3,  or  4,  as  the  case 


Ixxviii  SUGGESTIONS 

may  be.  Similarly  develop  the  fact  that  2J  ft.  =  |  ft., 
and  the  corresponding  rule.  So  also  for  thirds  and 
fourths.  Apply  your  rules. 

Lesson  59 

This  lesson  is  an  exercise  in  numeration  and  nota- 
tion, with  special  reference  to  Lesson  60,  and  should 
be  thoroughly  mastered.  Special  drill  should  be 
given  in  questions  like  12,  13,  14,  15. 

Lesson  60 

As  the  pupils  add  and  carry  or  subtract,  be  sure 
that  they  understand  the  place  value  of  the  different 
numbers.  Question  6  is  a  preparation  for  the  sub- 
traction that  follows  in  questions  7  and  8. 

Lesson  61 

When  such  questions  as  5  and  10  occur  in  this 
and  the  following  lessons,  frequently  have  the  pupils 
make  out  bills  neatly  and  accurately. 

Lesson  63 

Note  that  any  number  ending  in  0  or  5  is  divisible 
by  5.  As  in  question  6,  find  the  common  factor  of 
pairs  of  numbers  and  illustrate  its  meaning  by  meas- 
urement. To  bring  out  the  meaning  of  common 
factor  more  effectually,  select  a  unit  that  is  a  factor 
of  only  one  of  the  numbers  and  measure  the  corre- 
sponding qaantities  with  the  given  unit. 


SUGGESTIONS 

Lessons  66-68 

Lessons  66,  67,  68,  are  review  lessons.  If  any 
question  is  found  to  be  too  hard,  make  easier  ques- 
tions of  the  same  kind  leading  up  to  the  problem  in 
the  book. 

In  question  17,  page  141,  the  whole  quantity  is 
850,  the  number  is  5  and  the  unit  is  $10  (i.e.  $50 
-i-  5),  which  is  the  cost  of  the  chain.  In  Lesson  68, 
question  4,  the  pupil  is  given  the  unit  12^  and  the 
number  3J  to  find  the  quantity  3J  x  12  £  or  42^. 
The  following  are  the  two  questions  required  : 

(1)  At  12^  a  yd.,  how  many  yards  of  ribbon  will 
cost  42^? 

(2)  If  3|  yd.  of  ribbon  cost  42^,  what  is  the  cost 
per  yd.  ? 

Lesson  74 

The  method  of  finding  the  volume  of  a  prism  is 
indicated  in  question  1.  Count  again  first  by  2's, 
then  by  6's  (3  x  2).  Count  again  first  by  3's,  then 
by  12's  (4  x  3),  and  so  on.  Let  pupils  measure  the 
dimensions  of  prisms  in  the  room,  such  as  boxes, 
and  calculate  their  volumes.  What  units  of  volume 
have  we?  (1  cu.  in.,  1  cu.  ft.,  1  cu.  yd.,  1  cord.) 
Why  have  we  no  larger  unit  of  volume  than  1  cord  ? 

Lesson  76 

Develop  clearly  and  apply  in  practice  that  to  take 
f  of  128  you  divide  $28  by  7  and  multiply  the 


Ixxx  SUGGESTIONS 

quotient  by  3  ;  that  to  take  f  of  a  quantity,  you 
divide  the  quantity  by  8  and  multiply  the  quotient 
by  5 ;  that,  in  general,  to  take  a  fractional  part  of 
a  quantity,  you  divide  by  the  denominator  and 
multiply  by  the  numerator.  Can  you  first  multiply 
by  the  numerator  and  then  divide  by  the  denomi- 
nator ?  Show  instances  where  the  latter  method 
is  more  economical,  (f  of  $13,  |  of  $3|.)  See  that 
the  pupils  master  this  principle  and  are  able  to  use 
either  method  quickly  and  accurately. 

Lesson  77 

Develop  addition  and  subtraction  of  fractions  in 
the  order  indicated  in  Lessons  77,  78,  79.  Much 
oral  work  will  be  needed.  Have  the  pupils  illus- 
trate their  work  by  placing  dots  and  marking  them 
off  as  in  questions  8,  15,  19.  In  some  cases  verify 
by  actual  measurement.  Let  the  pupils  memorize 
the  simpler  sums  and  differences.  Let  the  work 
gradually  develop  into  the  more  generalized  form 
indicated  by  Lesson  78,  questions  9, 10,  11.  Finally, 
have  the  children  perform  the  simpler  operations 
mentally.  Throughout  the  oral  work  preceding 
these  lessons  give  and  let  the  pupils  give  many  illus- 
trative practical  examples. 

Lesson  80 

Many  interesting  and  practical  questions  may  be 
asked  in  connection  with  this  lesson.  Red  rasp- 


SUGGESTIONS  Ixxxi 

berries  are  sold  in  pint  boxes  because  they  would 
crush  if  put  up  in  quart  boxes.  Black  raspberries, 
gooseberries,  etc.,  being  firmer,  are  sold  in  quart 
boxes.  Why  are  strawberries  early  in  the  season 
frequently  sold  in  pint  boxes  ?  Which  is  the  fairer 
way  to  buy  and  sell  eggs,  by  the  pound  or  by  the 
dozen  ?  Why  ?  Illustrate  questions  13  and  14  by 
actual  measurement.  The  principles  rindicated  in 
question  22  are  important  and  of  frequent  appli- 
cation. 

Lesson  81 

Precede  this  lesson  in  sections  by  exercises  with 
the  class,  making  questions  similar  to  those  in  the 
lesson,  easier  at  first  but  gradually  becoming  more 
difficult.  Questions  5  and  6  illustrate  this  method. 

The  following  examples  relate  to  question  1 : 

What  quantity  is  measured  by: 

1.  The  number  4  and  the  unit  1  pt.?  (2  qt.) 

2.  The  number  4  and  the  unit  1  qt.  1  pt.?   (6  qt.) 

3.  The  number  4  and  the  unit  2  qt.  Ipt.?  (10  qt.) 

4.  The  number  6  and  the  unit  2  qt.  1  pt.?  (15  qt.) 

5.  The  number  8  and  the  unit  2  qt.?  (4  gal.) 

6.  The   number    8   and   the   unit    2   gal.    1  qt.? 
(18  gal.) 

7.  The   number   6   and   the   unit   1   gal.    2  qt.? 
(9  gal.) 

8.  Find  the  number  of  gallons  of  milk  in  6  cans, 
each  of  which  contains  2  gal.  2  qt. 


Ixxxii  SUGGESTIONS 

Lesson  86 

In  question  8  the  word  "accurately"  is  emphasized, 
because  while  it  is  important  that  pupils  should  work 
rapidly,  it  is  essential  that  their  work  should  be  accu- 
rate. The  question  to  the  class  should  be  not,  "  How 
many  questions  did  you  work  correctly  ?  "  but  "  How^ 
many  of  you  worked  correctly  every  question  that  you 
did?" 

Lesson  87 

If  pupils  are  to  master  long  division  so  that  they 
will  not  lose  time  in  guessing  in  a  haphazard  way  at 
the  successive  quotients,  they  must  become  expert  in 
the  use  of  the  trial  divisor  and  the  trial  dividend. 

Lesson  88 

In  questions  11  and  12  emphasize  the  place  value 
of  the  numbers.  $  29  divided  by  4  gives  $  7  as  quo- 
tient and  $  1  as  remainder.  $16  dimes  equals 
16  dimes.  16  dimes  divided  by  4  equals  4  dimes. 
4^  divided  by  4  equals  1^.  The  quotient  is  17.41. 
Similarly  with  the  long  division. 

Lessons  91-94 

These  lessons  indicate  the  method  of  teaching 
decimals.  First  make  use  of  the  pupil's  knowledge 
of  the  notation  and  numeration  of  dollars  and  cents. 


SUGGESTIONS  Ixxxiii 

Then  use  the  metric  stick,  since  a  practical  know- 
ledge of  it  is  useful  in  itself,  and  since  it  makes  the 
development  of  decimals  objective.  Pass  on  from 
this  to  quantities  expressed  in  terms  of  other  units 
of  measurement. 

Lesson  95 

Percentage  is  simply  a  special  case  of  fractions, 
and  should  be  so  taught.  A  quantity  divided  into 
fourths  is  measured  by  4  units,  and  each  part  is  ^  of 
the  quantity.  Three  parts  are  equal  to  f  of  the  quan- 
tity. Similarly  with  regard  to  quantities  divided 
into  fifths,  sixths,  etc.  A  quantity,  considered  in 
percentage,  is  divided  into  100  parts,  and  is  meas- 
ured by  100  units.  Each  part  is  yro  or  1  %  °f  the 
quantity,  and  5  parts  are  YOQ-  or  5 %  of  it.  On  the 
other  hand,  1  %  of  a  quantity  is  one-hundredth  of  it, 
and  5  %  is  five-hundredths  of  it. 

Lesson  100 

Section  XIII.  contains  questions  in  review.  They 
will  be  found  to  be  especially  helpful  in  preparing 
the  pupils  for  the  opening  chapters  of  the  "  Public 
School  Arithmetic." 


ARITHMETIC 

SECTION   I 

Lesson  1 

1.  Count  the  number  of  girls  in  your  room.     How 
many  ?    How  many  boys  ?    How  many  boys  and  girls  ? 

2.  Count  the  number  of  windows  in  the  room.    Of 
window  panes.     Of  windows  in  the  school  building. 

3.  Count  the  number  of  desks  in  your  room.     The 
number  that  are  not  occupied. 

4.  Count  the   number  of  boards   in   the  floor  of 
your  room  from  one  side  to  another. 

5.  Count  the  number  of  letters  in  this  example. 

6.  Count  the  number  of  pieces  of  crayon  in  a  box 
of  crayon. 

7.  Count   the   number  of  inches   in   a  foot.     Of 
inches  in  a  yard.     Of  feet  in  a  yard. 

8.  Measure  with  a  yardstick  and  count  the  num- 
ber of  yards  in  the  width  of  the  room.     In  the  length. 


2  ARITHMETIC 

9.  Count  the  number  of  steps  you  take  in  going 
from  one  side  of  the  room  to  the  other.  From  the 
front  to  the  back  of  the  room. 

10.  Measure  with  a  foot  rule  and  count  the  num- 
ber of  feet  in  the  width  of  the  room.     In  the  length. 

11.  How  many  yards  long  is  the  blackboard  ?    How 
many  feet?     How  many  feet  high? 

12.  How  many  inches  long  is  this  book?     How 
many  wide  ?     How  many  pages  does  it  contain  ? 

13.  How  tall  are  you?     How  old?     How  many 
pounds  do  you  weigh? 

14.  How  many  days  of  this  week  are  gone  ?     How 
many  days  of  this  month?     Weeks  of  this  month? 
How  many  months  of  this  year? 

15.  Fill   a   quart   measure  with   a  pint   measure. 
How  many  times  do  you  empty  the  pint  measure? 
How  many  pints  in  a  quart? 

16.  Fill  a  gallon  measure  with  a  quart  measure. 
How  many  quarts  in  a  gallon  ? 

17.  Fill  a  gallon  measure  with  a  pint  measure. 
How  many  pints  in  a  gallon  ? 

18.  How  many  pennies  in  a  nickel?     In  a  dime? 
In  a  25-cent  piece  ? 

19.  Count  on  a  clock  face  the  number  of  minutes 
in  a  quarter  of  an  hour.     In  half  an  hour.     In  three- 
quarters  of  an  hour.     In  one  hour. 


LESSON  2  B 

20.  Ask  your  teacher  to  make  raps  with  a  stick, 
strokes  with  a  bell,  or  to  pronounce  the  names  of 
letters.     Count  the  number  each  time. 

21.  How  can  you   get   the   expression  5   yd.  by 
measuring?     What  number  will  you  obtain  if  you 
measure  the  same  distance  with  a  foot  rule? 

22.  How  can  you  get  the  expression  3  qt.  by  meas- 
uring?    What  number  will  you  get  if  you  measure 
the  same  quantity  with  a  pint  ? 

Lesson  2 

1.  Count  the  pupils  in  the  first  two  rows  by  2's. 
How  many  2's?     Count  all  the  pupils  in  the  room 
by  2's.     How  many  2's? 

2.  Count  the  number  of  pairs  of  hands  in  the 
room.     How  many  pairs? 

3.  Count  the  pupils  in  groups  of  3.     How  many 
groups?     In  groups  of  4.     How  many  groups ? 

4.  Count  the  number  of  fingers  and  thumbs  in 
the  room  by  10's.     How  many  10's?     Count  by  5's. 
How  many  5's? 

5.  Count  the  number  of  pieces  of  crayon  in  a  box 
of  crayon  by  12's.     How  many  dozen  in  the  box? 

6.  Count  the  number  of  5-minute  spaces  in  one 
hour.     Of  10-minute  spaces.     Of  15-minute  spaces. 

7.  In  counting,  what  numbers  do  you  count  before 
the  number  4?     Before  6?     Before  10?     Before  15? 
Before  25? 


4  ARITHMETIC 

8.  Ask  your  teacher  to  make  taps  with  a  stick, 
strokes  with  a  bell,  or  to  pronounce  the  names  of  the 
letters  in  groups  of  2  or  3.     Count  the  number  of 
groups. 

9.  Count   12   pupils   by   2's.      How  many   2's? 
Count  by  6's.     How  many  6's?     By  3's.     How  many? 
By  4's.     How  many  ? 

10.   Count  18  pupils  by  3's.     By  6's.     By  2's.     By 
9's.     How  many  in  each  case  ? 


11.  Count  by  2's.     How  many  2's  in   8?    How 
many  2^  in  8^?     How  many  4's  in  8?    How  many 
4^  in  8^? 

12.  With  8^  how  many  lemons  can  you  buy  at  2^ 
each  ?     How  many  oranges  at  4  ^  each  ? 

13.  A  man  gave  2^  to  each  of  4  children.    How 
much  did  he  give  away?     How  many  pounds  in  4 
2-lb.  cans  of  corn  ? 

14.  How  many  2's  in  8?     What  is  one-fourth  of 
8?     What  is  ^  of  8  apples?    If  I  have  8  apples  and 
give  ^  of  them  away,  how  many  do  I  give  away? 
How  many  are  left? 

15.  How  many  4's  in  8?     What  is  one-half  of  8? 
There  are  8  trees  on  one  side  of  the  yard  and  \  as 
many  on  the  opposite  side.     How  many  are  on  the 
opposite  side? 


LESSON  3  5 

16.  Draw  a  line  2-in.  long.  Draw  another  line  2 
2-in.  long.  4  2-in.  long.  6  2-in.  long.  How  many 
inches  long  is  each  line? 

Lesson  3 

l.  Place  ten  dots.  How  many  2's  in  10?  How 
many  5's  in  10  ?  What  are  5  2's  equal  to  ?  What 
are  2  5's  equal  to  ? 

2.'  How  many  marbles  can  I  get  for  5  f  at  the  rate 
of  2  for  a  cent  ? 

3.  How  many  lead  pencils  at  2^  each  can  you 
buy  for  a  dime?     How   many   tablets   at  a  nickel 
apiece  can  you  buy  for  a  dime  ? 

4.  A  boy  picked   10   pt.   of  raspberries.     How 
many  quarts  did  he  pick  ? 

5.  A  coat  costs  $  10.     How  many  $2  bills  will  pay 
for  it  ?     How  many  $  5  bills  ? 

6.  How  many   2's  in  10?     What  is  one-fifth  of 
10?     James  paid  10^  for  a  ball  and  -J  as  much  for  an 
apple.     What  did  the  apple  cost  him  ?     What  did 
both  cost? 

7.  A  boy  earns  half  a  dollar  a  day.     How  much 
will  he  earn  in  10  da.  ? 

8.  If  it  takes  2  boys  5  hours  to  do  a  piece  of  work, 
how  long  would  it  take  one  boy  to  do  it  ?     Five  boys  ? 

9.  Place  twelve  dots.     Let  each  dot  represent  1  ^. 
How  many  2^  in  12^?     How  many  6^  in  12^?     At 
$2  a  bbl.  for  apples,  how  many  bbl.  for  1 12? 


6  ARITHMETIC 

10.  Let  each  dot  represent  1  pt.     What  unit  of 
measure  do  2  dots  represent  ? 

How  many  quarts  in  12  pt.?  How  many  pints  in 
6  qt.  ?  Out  of  a  pail  containing  12  pt.  of  water 
2  qt.  are  taken.  How  many  quarts  are  left  ? 

11.  How  many  qt.  in  2  pt.  ?     4  pt.  ?     6  pt.  ?     8  pt.  ? 
10  pt.  ?     How  many  pt.   in  1  qt.  ?     2  qt.  ?     3  qt.  ? 
4qt.?     5qt.? 

12.  How  much  will  a  man  earn  in  2  wk.  at  $  1  a 
day  ?     If  he  is  paid  in  two-dollar  bills,  how  many  bills 
does  he  get? 

13.  How  many  pounds  of  butter  are  there  in  6  2-lb. 
rolls  ?     In  2  5-lb.  pails  ? 

14.  How  many  2's  in  12?     What  is  one-sixth  of 
12  ?     How  many  inches  in  ^  of  a  foot  rule  ?     If  I 
have  $  12  in  my  purse  and  spend  J  of  it,  how  much 
do  I  spend?     How  much  have  I  left? 

15.  How  many  6's  in  12  ?     What  is  one-half  of  12  ? 
What  will  half-a-dozen  eggs  cost  at  2  f  each  ? 

16.  Count  12  dots  by  4's.     How  many  4's  in  12? 
What  is  one-third  of  12?     What  is  one-fourth  of  12? 

If  I  pay  $12  for  3  bbl.  of  flour,  what  is  the  cost 
per  barrel ? 

17.  Make  simple   practical  questions   illustrating 
Jof  8^  =  4^,  and  1  of  10  =  5. 


LESSON  4  7 

Lesson  4 

•  •    •    •    • 

•  •    •    •    • 

1.  Count  these  dots  by  3's.     How  many  3's  in  15  ? 
How  many  5's  in  15  ? 

2.  If  each  dot  represents  1  ft.,  what  unit  do  3 
dots  represent  ? 

How  many  yards  in  15  ft.  ? 

3.  Draw  lines  dividing  these  15  dots  into  5  equal 
parts.     What  is  \  of  15  ?     What  is  £  of  15  ? 

Paid  15  dimes  for  5  yd.  of  cloth,  what  was  the 
price  per  yard  ? 

4.  An   overcoat  was   paid  for  with  3  five-dollar 
bills.     How  many  dollars  did  it  cost  ? 

5.  Count  the  number  of  2-in.  lengths  in  a  yard. 
How  many  ?     How  many  3-in.  in  36  in.  ?     How  many 
12-in.  in  36  in.?     How  many  4-in.  in  36  in.?     How 
many  9-in.  ?     How  many  6-in.  ? 

6.  What  is  the  cost  of  3  pt.  of  molasses,  at  12^ 
apt.? 

In  36  eggs  how  many  dozen  ? 

7.  If  I  work  9  hr.  a  day,  how  many  hours  shall  I 
work  in  4  da.  ? 

If  1  Ib.  of  raisins  cost  9^,  how  many  pounds  can 
you  buy  for 


8  ARITHMETIC 

8.  Measure  two  points  15  in.  apart.      Measure 
this  distance  with  3-in.  and  5-in.  units.     How  many? 

Measure  two  points  18  in.  apart  with  2-in.,  9-in., 
3-in.,  6-in.  units.  How  many? 

9.  Make  simple,  practical  questions  like  questions 
6  and  7. 

10.  Cut  out  of  cardboard  a  unit  3  in.  long;  use 
this  unit  to  measure  a  line  9  in.  long.     How  many 
3  in.  in  9  in.  ? 

How  many  3  ^  in  9  ^  ?  3  dimes  in  9  dimes  ?  3  Ib. 
in  9  Ib.  ?  At  3  #  a  yard,  how  many  yards  of  tape  can 
you  buy  for  9  ^  ? 

11.  Use  the  3-in.  unit  to  measure  lines  respectively 
12  in.,  18  in.,  24  in.,  30  in.,  36  in.  long.     How  many 
3-in.  units  in  each  case?     How  many  3  oranges  in  12 
oranges?     In  18  oranges?     How  many  cents  in  8 
3-ct.  ?    In  10  3-ct.  ? 

12.  A  boy  divided   12  oranges  among  his  play- 
mates, giving  3  oranges  to  each.     How  many  play- 
mates were  there? 

13.  What  will  6  lemons  cost,  at  3^  apiece?    At 
3^  each,  how  many  lemons  can  you  buy  for  24^? 

14.  Cut  out  of  cardboard  a  unit  4  in.  long ;  use  it 
to  measure  a  line  8  in.  long.     How  many  4-in.  in  8 
in.  ?     How  many  4-ct.  in  8  ct.  ?     How  many  cents  in 
24-ct.?    In42-ct.? 

15.  What  will  2  hats  cost  at  $4  each  ?    How  many 
apples  at  2^  each  can  you  buy  for 


LESSON  5  9 

16.  Use  the  4-in.  unit  to  measure  lines,  respectively, 
16  in.,  24  in.,  32  in.  long.     How  many  4-in.  units  in 
each  case?     How  many  4^  in  24^?      How  many 
cents  in  4  4  f  ?     How  many  miles  in  6  4-mi.  ? 

17.  How  many  pounds  of  soap,  at  4^  a  pound,  can 
you  buy  for  24  $  ?     How  far  will  a  man  walk  in  6  hr., 
at  the  rate  of  4  mi.  an  hour  ? 

18.  Use  the  5-in.  unit  to  measure  lines,  respec- 
tively, 15  in.,  20  in.,  30  in.,  35  in.  long.     Use  the  6-in. 
unit  to  measure  lines,  respectively,  12  in.,  24  in.,  36 
in.     Into  how  many  parts  has  each  been  divided  ? 

15  in. -5- 5  in.  =  ?  24  in.  •*•  6  in.  =  ?  25  in.  -f-  5  in.  =  ? 

19.  Divide  a  line  12  in.  long  into  2  equal  parts. 
How  long  is  each  part  ?     Into  3  equal  parts.     Into  4. 
Into  6.     How  long  is  each  part  in  each  case  ?     What 
is  \  of  12  in.?   \  of  12  in.?   \  of  12  in.?   \  of  12  in.? 

20.  What  is  the  meaning  of  18  in. -f- 3  in.  =  6? 
Of  \  of  18  in.  =  6  in.?     Of  18  in.  -5-3  =  6  in.? 

21.  Can  you  exactly   measure  a  line  23  in.  long 
with  a  2-in.  unit?     3-in.  unit?     4-in.  unit?     5-in. 
unit?     6-in.  unit? 

What  remainder  in  each  case  ? 

Lesson  5 


1.   With  a  piece  of  paper  cover  all  of  these  dots 
but  one,    How  many  do  you  see  ?    How  many  are 


10  AHI FHMETIC 

covered?  What  must  be  done  with  1  to  get  4? 
With  1^  to  get  4^?  With  1  dime  to  make  4  dimes? 
With  a  line  2  in.  long  to  get  a  line  4  2-in.  long? 
With  1  5-dollar  bill  to  get  4  5-dollar  bills? 

2.  Cover  all  the  dots  but  2.     How  many  do  you 
see?     How  many  are  covered?     What  must  be  done 
with  2  to  get  4? 

I  have  2  doz.   eggs.     How  many  must  I  buy  to 
have  4  doz.  ? 

3.  I  have  4  dimes,  and  pay  10^  for  a  yard  of  cot- 
ton.    How  many  dimes  have  I  left? 

A  gallon  measure  contains  3  qt.  of  water.     How 
much  must  I  pour  in  to  fill  it? 


4.  Cover  all  these  dots  but  1 ;  all  but  2 ;  all  but 
3 ;  all  but  4.      In  each  case  how  many  do  you  see  ? 
How  many  are  covered? 

5.  I  want  to  give  an  apple  to  each  of  5  boys.     If  I 
have  3  apples,  how  many  more  must  I  get  ? 

6.  I  buy  a  2-ct.  postage  stamp.     What  change  do 
I  get  back  from  a  nickel  ? 

Bought  2  yd.  of  cloth,  at  $  2  a  yard.     What  change 
do  I  get  out  of  a  5-dollar  bill  ? 

7.  Draw  a  line  one  part  of  which  is  3  2-in.  long 
and  the  other  2  2-in.  long.     How  many  2  in.  in  the 
length  ?     How  many  inches  ? 


LESSON  5  11 

8.  I  paid  $1  for  a  pair  of  gloves  and  2  two-dollar 
bills  for  a  pair  of  shoes.     What  did  both  cost? 

9.  Mary  was  at  school  on  Thursday,  but  was  kept 
at  home  the  rest  of  the  week  on  account  of  illness. 
How  many  days  was  she  absent? 


10.  Cover  all  the  dots  but  5  ;  all  but  4  ;  all  but  3  ; 
all  but  2;  all  but  1.     In  each  case  how  mairy  do  you 
see  ?     How  many  are  covered  ?     Practise  this  until 
you  can  do  it  correctly  and  quickly. 

11.  I  spent  16  for  a  hat  and  a  pair  of  shoes.     If 
the  hat  cost  $2,  what  did   the  shoes  cost?      Three 
rolls  of  butter  weighed  6  Ibs.     What  was  the  average 
weight  per  roll  ? 

12.  A  grocer  has  6  50-lb.  sacks  of  flour  and  sells  3 
of  them.     How  many  sacks  has  he  left  ? 

13.  How  many   3-lb.   packages   of   wafers   weigh 
6  lb.?      6  10-dollar  bills  are  changed  for  20-dollar 
bills  ;  how  many  20's  are  received  ? 


14.  How  many  dots  all  together  ?  Cover  all  but 
6  ;  all  but  5  ;  all  but  4  ;  all  but  3  ;  all  but  2  ;  all 
but  1.  In  each  case  how  many  do  you  see  ?  How 
many  are  covered  ?  Practise  this  until  you  can  do  it 
quickly  and  accurately. 


12  AEITHMETIC 

15.  A  boy  has  7  mi.  to  go.     If  he  rides  5  mi.,  how 
far  does  he  walk  ? 

16.  The  sum  of  what  two  numbers  equals  7  ? 

17.  Henry  had  7  marbles  and  lost  4  of  them;  how 
many  had  he  left  ? 

18.  A  boy  has  7  dimes  and  buys  3  collars  at  10^ 
each.     How  many  dimes  has  he  left? 

19.  On  Wednesday  morning  how  many  days  of 
the  week  are  gone  ?     How  many  are  still  left. 

20.  How   many  nickels    will    pay   for    5    2-cent 
postage   stamps?     How   many   dimes   will   pay  for 
10  apples  at  1  f  each  ?     How  many  25-ct.  pieces  will 
pay  for  25  lemons  at  3^  each? 

21.  I  have  7  25-ct.  pieces  and  buy  25  one  cent 
stamps.     How  many  handkerchiefs  can  I  buy  with 
the  remainder  at  25  f  each  ? 

22.  I  have  7  nickels  and  buy  5  apples  at  2^  each. 
How  many  nickels  have  I  left  ? 

23.  Seven  10-dollar  bills  are  changed  for  5-dollar 
bills,  how  many  5's  are  received  ? 

Lesson  6 


•    •    •    • 

1.  How  many  dots  all  together?  Cover  all  but 
7 ;  all  but  1 ;  all  but  6 ;  all  but  2 ;  all  but  5 ;  all 
but  3 ;  all  but  4.  In  each  case  how  many  do  you 
see?  How  many  are  covered? 


LESSON  6  13 

2.  A  grocer  has  8  6-lb.  boxes  of  starch,  and  sells 
3  of  them.     How  many  has  he  left? 

3.  How  many  pairs  of  two  in  eight? 

4.  If  I  carry  home  a  parcel  containing  a  3-lb.  can 
of  tomatoes  and  5  Ib.  of  sugar,  what  is  the  weight 
of  my  parcel  ? 

5.  At  2  dimes  a  dozen,  how  many  eggs  for  8 
dimes  ?     How  many  hours  will  it  take  a  man  walk- 
ing 4  miles  an  hour,  to  go  8  miles? 


6.  What  must  be  done  with  8  dots  to  make  9 
dots  ?     This  did  what  with  4  of  the  8  dots  ? 

7.  Cover  all   these   dots   but  9;   all  but  8;   all 
but  7;   all  but  6;   all  but  5;   all  but  4;  all  but  3; 
all  but  2 ;   all  but  1.     In  each  case  how  many  do 
you  see  ?     How  many  are  covered  ? 

8.  A  child  is  4  yr.  of  age.     In  how  many  years 
will  it  be  9? 

9.  6  is  one  more  than  what  number  ?     One  less 
than  what  number?     7  is  one  more  than  what  num- 
ber?    One  less  than  what  number?     8  and  9  are 
each  one  more  than  what  number?     One  less  than 
what  number  ? 

10.   9  boys  were  skating  and  3  went  home  at  5 
o'clock.     How  many  remained  ? 


14  ARITHMETIC 

11.  How  many  3  in.  in  9  in.?  3  ft.  in  9  ft.?  3 
dimes  in  9  dimes  ?  3  5-dollars  in  9  5-dollars  ?  3  tens 
in  9  tens  ? 


12.  If  each  dot  represents  1  ^,  what  unit  of  money 
do  all  represent  ?     How  many  nickels  ? 

13.  Cover  all   these   dots   but  9 ;   all   but   1 ;   all 
but  8  ;  all  but  2 ;  all  but  7 ;  all  but  3 ;  all  but  6  ;  all 
but  4 ;   all  but  5.     In  each  case  how  many  do  you 
see?     How  many  are  covered? 

14.  How  many  5's  do  you  see  in  10  ?     How  many 
2's?     How  many  oranges  at  5^  apiece  can  you  buy 
for  one  dime  ?     How  many  eggs  at  2  ^  each  ? 

15.  If  I  pay  7  f  for  a  cake  of  sapolio,  what  change 
do  I  get  back  from  a  dime  ? 

16.  What  is  the  cost  of   2  cakes  of  soap   at  4^ 
apiece  and  a  yeast  cake  at  2^? 

17.  What  is  the  weight  of  2  3-lb.  cans  of  corn  and 
3  1-lb.  cans  of  peas  ? 

18.  A  line  10  in.  long  is  divided  into  5  equal  parts. 
How  long  is  each  part  ?     Draw  the  line. 

19.  With  ten  dimes  how  much  butter  can  be  bought 
at  two  dimes  a  pound  ?     Bought  flour  at  $5  a  barrel 
and  paid  for  it  with  a  ten-dollar  bill.     How  many 
barrels  ? 

20.  How  many  f  2  in  $10?    2ft.  in  10  ft?    Smiles 
in  10  miles?     5  ten-dollar  bills  in  10  ten-dollar  bills? 


LESSON  7  15 

21.  If  I  bought  two  lead  pencils  at  4^  each  and  an 
eraser  for  2  ^,  what  did  all  cost  ? 

22.  How  many  5-cent  pieces  make  50  X? 

I  gave  James  one  dime  and  Robert  ^  as  much. 
What  did  I  give  Robert?     What  did  I  give  both? 

23.  I  divided  10  quarter-dollars  equally  among  5 
children.    What  did  each  receive  ?    How  many  cents  ? 

24.  How  many  strips  of  wall  paper,  each  2  ft.  wide, 
will  be  needed  for  the  side  of  a  room  10  ft.  in  width  ? 

25.  I  have  a  dime  and  buy  a  tablet  for  4  ^.     How 
many  yards  of  ribbon  at  3  ^  a  yd.  can  I  buy  with  the 
change  ? 

Lesson  7 

1.  How  many  cents  in  2  dimes?     4  dimes?     5 
dimes  ?  .  8  dimes  ? 

What  will  6  yd.  of  ribbon  cost  at  one  dime  a  yard? 

2.  How  many  cents  in  3  dimes  2^  ?    6  dimes  4^? 
7  dimes  1  nickel? 

I  gave  6  dimes  and  3  ^  for  a  book.     How  many 
cents  did  it  cost? 

3.  I  paid  3  ten-dollar  bills  and  a  five-dollar  bill 
for  a  cow.     How  many  dollars  did  the  cow  cost  me  ? 

4.  How  many  dimes  in  40^?     60  £?     90^?     How 
many  dimes  and  cents  in  24^?     56^?     89^? 

I  paid  in  dimes  and  cents  23^  for  a  comb.     How 
many  of  each  did  I  pay,  there  being  5  coins  in  all? 


16  ABITHMETIC 

5.  I  paid  in  dimes  and  nickels  75  ^  for  a  pair  of 
gloves.     How  many  of  each  did  I  pay,  there  being  8 
coins  in  all  ?     How  many  of  each,  there  being  9  coins 
in  all? 

6.  What  unit  of  money  is  equal  in  value  to  2  dimes 
and  a  nickel  ?     5  dimes  ?     10  dimes  ?     20  dimes  ? 

7.  I  have  2  dimes.     How  many  dimes  must  I  put 
with  these  to  be  able  to  exchange  them  for  half-a- 
dollar? 

30  mi.  +  6  mi.  =  ?  mi.     20  mi.  +  8  mi.  =  ?  mi. 

8.  A  man  drove  ten  miles  an  hour  for  4  hr.  and 
then  walked  2  mi.     How  far  did  he  go  ? 

9.  A  lady  bought  a  rug  for  4  ten-dollar  bills,  a 
desk  for  2  ten-dollar  bills,  and  a  chair  for  $8.     What 
did  all  cost  her  ? 

10.  A  grocer  had  9  10-lb.  sacks  of  flour  and  sold 
6  of  them.     How  many  had  he  left,  and  how  many 
pounds  did  they  weigh  ? 

11.  The  minute  hand  of  a  clock  moves  through  5 
10-min.  spaces  and  3  10-min.  spaces  in  how  many 
minutes  ? 

12.  The    thermometer   registers    4    ten    degrees. 
Through  how  many  ten  degrees  must  the  temperature 
rise  to  register  7  ten  degrees?     How  many  degrees 
will  it  then  register? 

13.  A  boy  has  $1  and  spends  4  dimes.    How  much 
has  he  left? 


LESSON  8  17 

14.  From  85  Ib.  of  flour  how  many  10-lb.  sacks  can 
be  put  up,  and  how  many  pounds  will  be  left  over  ? 

15.  64  gal.  are  equal  to  6  ten-gallons  and  4  gal. 
Read  the  following  in  the  same  way :  32  yr. ;  27  da. ; 
43  min. ;  58  mi. ;  64  Ib. ;  25  qt. 

16.  Write  in  figures  and  use  contractions :  Twenty- 
five   cents ;   ninety-four   dollars  ;   sixty-six   gallons ; 
eighty  quarts ;  sixteen  years ;  thirty-one  days. 

17.  Write  in  figures  :   Fourteen  ;  fifty-five  ;  forty ; 
ninety-one ;  twenty-eight. 

18.  What  number  is  equal  to 

2  +  10?  3  +  10?  4  +  10?  5  +  10? 
8  +  10?  9  +  10?  20+  2?  30+  4? 
5  +  40?  6  +  60?  7  +  80?  9  +  90? 

19.  Harriet  is  3  yr.  old  and  her  sister  Caryl  10. 
What  is  the  sum  of  their  ages  ? 

20.  How  many  cents  in  a  nickel  and  a  dime  ? 

21.  A  man  bought  4  Ib.  of  lump  sugar  and  20  Ib. 
of  granulated.     How  many  pounds  of  sugar  did  he 
buy? 

Lesson  8 

1.  What  is  the  cost  of  3  yd.  of  lace  at  2  dimes  a 
yard  ?     How  many  cents  ? 

2.  How  many  dimes  in  20^? 

How  many  yards  of  ribbon  at  20^  a  yd.  can  you 
buy  for  8  dimes  ? 

3.  What  is  the  cost  of  2  gal.  of  syrup  at  5  dimes 
a  gallon  ?     How  many  dollars  ? 


18  ARITHMETIC 

4.  If  8  2-lb.  cans  of  fruit  cost  9  dimes,  how  many 
dimes  will  one  can  cost?     How  many  cents? 

5.  What  will  10  Ib.  of  canary  seed  cost  at  J  dime 
per  pound? 

6.  A  lady  bought  4  yd.  of  ribbon  at  2  dimes  a 
yard,  and  two  bunches  of  tape  for  6^.     How  many 
cents  did  both  cost? 

7.  I  paid  25  ^  for  a  handkerchief  and  a  spool  of 
thread.     If  the  handkerchief  cost  2  dimes,  what  did 
the  thread  cost? 

8.  A  lady  spent  5  ten-dollar  bills  for  a  sofa,  a  five- 
dollar  bill  for  a  chair,  2  ten-dollar  bills  for  a  table. 
How  much  did  she  spend  in  all  ? 

9.  I  bought  a  horse  for  $200  and  3  cows  at  1 30 
each.     What  did  all  cost? 

10.  A  farmer  sold  horses  for  $600,  cows  for  $80, 
and  a  sheep  for  $  6.     How  much  did  he  receive  for 
all? 

11.  645  gal.  are  equal  to  6  one  hundred-gal.,  4  ten- 
gal.,  and  5  gal.     Read  the  following  in  the  same  way : 
432  yr. ;  227  da. ;  543  min. ;  258  mi. ;  164  Ib. ;  325  qt. 

12.  Write  in  figures  and  use  contractions:   Three 
hundred  twenty-four  dollars  ;  one  hundred  thirty-four 
miles ;   six  hundred  forty  acres ;   five  hundred  four 
years ;  nine  hundred  ninety-nine  years  ;  seven  hun- 
dred   three    pounds ;    one    thousand    dollars ;    two 
thousand  dollars ;  three  thousand  dollars. 


LESSON  8  19 

13.  Write    in    figures :    Six    hundred    forty-nine ; 
two  hundred  fifty;  eight  hundred  fifty;  three  hun- 
dred  thirteen ;    seven   hundred  fifty ;   six   hundred 
five. 

14.  100  +  62  =  ?      200  +  45  =  ?      300  +  17  =  ? 

200  +  50  +  4  =  ?  6  +  40  +  100  =  ? 

300  +  40  +  5  =  ?  2  +  10  +  200  =  ? 

15.  A  man  weighs  200  Ib.  and  his  son  64  Ib.    What 
is  the  sum  of  their  weights  ? 

16.  If  I  paid  $3  for  a  hat,  $20  fora  suit  of  clothes, 
and  $100  for  two  rugs,  what  did  all  cost? 

17.  I  paid  |300  for  a  piano,  1 40  for  a  sofa,  and  $8 
for  a  chair.     What  was  the  cost  of  all  ? 

18.  How  many  cents  in  a  dime  ?   Dimes  in  a  dollar  ? 
How  many  single  units  in  a  ten-unit?     Ten-units  in 
a  hundred-unit? 

19.  A  farmer  sold  a  horse  for  one  hundred  dollars, 
a  cow  for  thirty  dollars,  and  a  sheep  for  six  dollars. 
What  did  he  get  for  all? 


SECTION  II 
Lesson  9 


Add: 

1. 

3  in. 

3  in. 

3  in. 

3  in. 

2  " 

12  « 

22  " 

32  " 

2.    What  is  the  sum  of  32  in.  and  3  in.  ? 

James  can  take  a  step  32  in.  long  and  John  3  in. 
farther.  How  far  can  John  step?  Draw  a  line  on 
the  board  and  mark  off  the  two  steps. 


3. 

3  min. 

3  min. 

3  min. 

3  min. 

2    " 

12    " 

22    " 

32    " 

3  min. 

3  min. 

3  min. 

3  min. 

42    " 

52    « 

62    " 

72    " 

4.  22  min.  -f  3  min.  =  ?  min.     42  min.  +  3  min.  = 
?  min. 

Agnes  takes  22  min.  to  learn  her  lesson,  and  Mary 
3  min.  longer.     How  long  does  Mary  take  ? 

5.  3  ft. 
2  " 


LESSON  9  21 

6.  3^                   3^                  3^  3<* 

2^                  12^                 22^  42^ 

7.  George  paid  3^  for  an  orange  and  12^  for  a 
pound  of  nuts.     What  did  both  cost  ? 

8.  2  in.                 2  in.                2  in.  2  in. 
3  "                13  "                23  "  32  " 


9. 


2 

in. 

2 

in. 

1 

in. 

2 

in. 

43 

M 

53 

44 

63 

44 

73 

44 

2 

min. 

2 

min. 

2 

min. 

2 

min. 

3 

tt 

13 

44 

23 

44 

32 

44 

2 

min. 

2 

min. 

2 

min. 

2 

min. 

43 

u 

50 

44 

73 

44 

93 

44 

10.  333333333 
212223142526072      82 

11.  222222222 
3      11       23       33      42      53      63      73      80 

12.  323232322 
2        3      12      13      22      23      32      33      42 

13.  Harry  paid  twenty -three  cents  for  a  book,  and 
two  cents  for  an  eraser.     What  did  both  cost  ? 

14.  Add  3  to  each  of  the  following  numbers,  and 
read  their  sums  :  2,  12,  22,  32,  42,  52,  62,  72,  82,  92. 
Memorize  these  results. 


22  ARITHMETIC 

15.  Add  2  to  each  of  the  following  numbers,  and 
read  their  sums  :  3,  13,  23,  33,  43,  53,  63,  73,  83,  93. 
Memorize  these  results. 

16.  What  is  the  sum  of   3  1-cent  pieces  and  2 
1-cent   pieces?      Of   3  5-cent   pieces   and    2   5-cent 
pieces  ?     Of  3  10-cent  pieces  and  2  10-cent  pieces  ? 
Of  3  units  of   any  kind  and  2  units  of    the  same 
kind  ? 

17.  What  is  the  sum  of  2  half-dollars  and  3  half- 
dollars  ?    Of  2  quarter-dollars  and  3  quarter-dollars  ? 

18.  Draw  two  lines,  end  to  end,  one  3  2-in.  long 
and  the  other  2  2-in.  long.     How  many  2-in.  in  the 
sum  of   their  lengths?     How  many  inches?     How 
many  2-in.  in  10-in.  ? 

19.  Measure  with  a  ruler  the  length  of  this  book. 
How  many  inches  long  is  it  ?    One  inch  is  called  the 

unit  of  measure. 

20.  How  many  cents  did  this  book  cost  ?     One 
cent  is  the  unit  that  measures  the  cost  of  this  book. 

21.  Measure    the   blackboard   with    the    pointer. 
How  many  pointers  long  is  it  ?     Measure  it  with  a 
twelve-inch  rule.     How  many  12-in.  in  its  length  ? 

22.  What  unit  of   measure  did  you  use  in  each 
case  above  ? 

23.  Harry,  how  would  you  proceed  to  measure  the 
height  of  Charlie  ?     What  units  of   measure  would 
you  use  ? 

24.  What  use  do  we  make  of  these  different  units  ? 


LESSON   10 


Add: 
l.      1  in. 


2. 


Lesson  10 


lin. 
14  « 


1  min.       1  min. 
4    "         14    " 


lin. 
24  " 


lin, 
33  " 


1  in, 
44  " 


1  min.       1  min.       1  min. 

22    "        34    "         44    " 


1  min.       1  min.       2  min.       1  min.       1  min. 

54    "        60    "        72    "        84    "        94    " 


3.      1  ft. 


1ft. 
14  " 


1  yd.         1  yd. 


14   " 


21    " 


1  mi. 

24   " 


4.  Two  boys  run  a  race  ;  the  first  runs  24  yd.,  and 
the  second  comes  in  1  yd.  ahead.  How  many  yards 
does  the  second  boy  run  ? 

f  It  Zf  II  81 

^  24^  41^  $44  154 


5. 


6.  A  man  paid  $34  for  a  suit  of  clothes  and  f  1  for 
a  necktie.  What  did  both  cost?  What  three  bills 
would  pay  for  both  ? 


7. 


4  in. 
1  " 


4  in. 
11  " 


4  in. 

20  " 


4  in. 
31  " 


2  in. 
41  " 


8.  I  took  11  min.  to  walk  to  the  depot  and  then 
had  to  wait  4  min.  for  the  train.  How  many  min- 
utes before  train  time  did  I  leave  home  ? 


24  ARITHMETIC 

9.    4  min.       4  min.       4  min.       4  min.       4  min. 
1    "        11    "        21    "        31    "        41    " 

10.  Add  1  to  each  of  the  following  numbers,  and 
read  their  sums :    4,  14,  24,  34,  44,  54,  64,  74,  84,  94. 
Memorize  these  results. 

11.  Add  4  to  each  of  the  following  numbers,  and 
read  their  sums :    1,  11,  21,  31,  41,  51,  61,  71,  81,  91. 
Memorize  these  results. 

12.  What  is  the  sum  of  4  half -hours  and  1  half- 
hour?     Of  1  5-lb.  pail  of  butter  and  4  5-lb.  pails  of 
butter?     Of  4  2-lb.  rolls  of  butter  and  1  2-lb.  roll  of 
butter  ?     Of  4  units  of  any  kind  and  1  unit  of  the 

same  kind? 

c 

A I 


13.  The  distance  from  A  to  B  is  25  miles;  the 
distance  from  B  to  C  is  4  miles.  How  far  is  it  from 
A  to  C  ?  What  unit  was  used  to  measure  the  dis- 
tance from  A  to  B  ?  From  A  to  C  ? 

•    •  I  •  • 


14.  Read  these  dots  from  left  to  right,  and  also 
from  right  to  left.     Thus,  5  =  4  +  1,  or  1  +  4. 

15.  Make  5  dots  and  draw  lines  through  them  in 
any  direction.     Read  your  results. 

16.  What  two  numbers  give  5  when  added?    15? 
25?  35?  45? 


LESSON   11  25 

17.  A  boy  is  5  ft.  high.     What  unit  is  used  to 
measure  his  height? 

18.  November  7  William  was  12  mo.  old,  how  old 
will  he  be  Feb.  7  of  the  next  year  ? 

19.  With  a  yardstick  measure  a   piece  of  string 

3  yd.  long.     Measure  it  again  with  a  foot  rule  and 
count  the   number   of  times   you   measure.     What 
number  did  you  get?     3  yd.  =  ?  ft. 

20.  Measure  a  piece  of  string  4  ft.  long  with  a 
unit  half-a-foot  long.     What  number  did  you  get? 

4  f t.  =  ?  half-feet. 

21.  Draw  two  lines,  end  to  end,  one  4  3-in.  long, 
and  the  other  1  3-in.  long.     How  many  3-in.  in  the 
sum   of  their  lengths?     How  many  inches?     How 
many  3-in.  in  12  in.  ? 

22.  Measure  the  length  of  a  table.     What  unit  or 
units  did  you  use? 

23.  How  long  is  your  morning  recess?     What  is 
the  unit  that  measures  the  length  of  your  recess? 

Lesson  11 

1.  2  in.  +  3  in.  =  ?  in.  2  in.  -f  ?  in.  =  5  in. 
3  in.  +  2  in.  =  ?  in.  3  in.  -f  ?  in.  =  5  in. 

2.  4^  +  1^  =  5^  4^+?^  =  5^ 
1^  +  4^  =  5^  l^  +  ?^  =  5£ 

3.  3 -h?  =  5  4+?  =  5 
l+?  =  5  2+?=5 


26  ARITHMETIC 

4.  James  had  2^,  and  his  father  gave  him 
How  many  cents  did  he  then  have  ? 

5.  Harry  had  12  marbles  and   found  3.     How 
many  did  he  then  have? 

6.  A  man  travelled  24  mi.  by  train  and  walked 

1  mi.     How  far  did  he  go  ? 

7.  I  paid  |5  for  a  hat  and  a  pair  of  gloves.     The 
hat  cost  $4.     What  did  the  gloves  cost? 

8.  I  bought  a  book  for  22^  and  a  pencil  for  3^. 
What  did  I  pay  for  both? 

9.  I  gave  a  quarter  of    a  dollar  for  a  yard  of 
ribbon  and  received  2^  in  change.     What  did  the 
ribbon  cost  me? 

10.  12  +  ?  =  15          22  +  ?  =  25          ?  +  3  =  25 
32  +  ?  =  35  ?  +  3  =  45          ?  +  3  =  15 

11.  I  paid  $25  for  a  suib  of  clothes  and  a  pair  of 
shoes.     I   paid  1 22   for  the   suit.     What   did   the 
shoes  cost? 

12.  Take  two  points  2  yd.,  3  yd.,  and  again  4  yd. 
apart.     Measure  each  of  these  distances  with  a  foot 
rule.      What   numbers   do   you   get?      1  yd.  =  ?  ft. 

2  yd.  =  ?  ft.     3  yd.  =  ?  ft.     4  yd.  =  ?  ft.     5  yid,  =  ?  ft. 

13.  Measure  two  points  1  yd.  2  ft.  apart,  2  yd.  1  ft. 
apart,  and  again  3  yd.  2  ft.     Measure  each  of  these 
distances   again  with   a   foot   rule.     What  numbers 
do   you  get?     1  yd.  2  ft.  =  ?  ft.     2  yd.  1  ft.  =  ?  ft. 

3  yd.  2  ft.  =  ?  ft.     4  yd.  1  ft.  =  ?  ft. 


LESSON   11  27 

14.  Measure  the  length  of  things  in  the  room  as 
the  table  in  yards  and  feet,  and  again  in  feet. 

15.  Find  by  measuring  the  number  of  yards  and 
feet  in  8  ft. ;  14  ft. ;   16  ft. ;  20  ft. 

16.  What  units  does  the  milkman  use  to  measure 
milk? 

17.  Put  3  qt.  of  water  into  a  pail.     Measure  this 
again  with  a  pint  measure,  and  count  as  you  do  this. 
What  number  do  you  get?     Do  the  same  with  4  qt. 
of  water.     1  qt.  =  ?  pt.     2  qt.  =  ?  pt.     3  qt.  =  ?  pt. 
4  qt.  =  ?  pt.     5  qt.  =  ?  pt. 


18.  How  many  dots  ?     Count  by  twos.     How  many 
twos?     If  each  dot  represents  1  pt.,  what  do  2  dots 
represent  ?     How  many  pints  are  represented  ?     How 
many  quarts? 

19.  Place  dots  to  represent  4  pt.  of  water  in  a  pail. 
6  pt.,  8  pt.,  10  pt.,  12  pt.     How  many  quarts  are 
represented  each  time? 

20.  4  pt.  =  ?  qt.  6  pt.  =  ?  qt.  8  pt.  =  ?  qt. 

10  pt.  =  ?  qt.  12  pt.  =  ?  qt. 

21.  A  line  is  measured  by  the  unit  2  in.  and  the 
number  6.    How  many  inches  long  is  the  line  ?    Draw 
it.     With  the  unit  3  in.,  what  number  would  measure 
its  length  ?    With  the  unit  4  in.  ? 


28  ARITHMETIC 

Lesson  12 


. 

Add: 

1. 

1  min. 

1  min. 

1 

min.         1 

min. 

1  min. 

5    " 

15    " 

25 

35 

u 

45    " 

2. 

5^ 

5^ 

4^ 

5* 

5* 

5^ 

iy 

11* 

21* 

31  £ 

40  J* 

51* 

3.  15  min.  +  ?  min.  =  16  min. 

1  min.  +  ?  min.  =  16  min. 

A  boy  takes  16  min.  to  walk  to  school.  If  he  is 
1  min.  late,  how  many  minutes  before  school  time 
did  he  leave  home  ? 

4.  Harry  has  31  ^,  and  his  brother  5  £  How  much 
have  they  together  ? 


5.   1 

1 

3 

1 

1 

5 

55 

65 

72 

85 

95 

41 

5 

5 

2 

5 

5 

5 

50 

61 

72 

81 

91 

11 

6.   Five   years   ago  a  young  man  was  twenty-one 
years  old.     What  is  his  age  at  present  ? 


•    •  •    • 


7.    Read  these   dots  from   left  to  right  and  also 
from  right  to  left. 


LESSON  12  29 

8.  Read  your  answer  to  question  6  again,  letting 
each  dot  represent  one   dime,  one   half-dollar,   one 
2-lb.  package  of  oatmeal,  one  3-qt.  can  of  peas. 

9.  What   is    the   meaning   of    5  +  1  =  6  ?      Of 
4  +  2  =  6?    Of  3  +  3  =  6? 

10.  Make  6  dots  and  draw  lines  through  them  in 
any  direction.     Read  your  results. 

11.  Memorize : 

15243 
51423 

666  66 

12.  What  is  the  value  of  one  nickel  and  1  penny  ? 
Of  one  five-dollar  bill  and  $1  ? 

13.  What  is  the  weight  of  3  2-lb.  packages  of  cakes 
and  3  2-lb.  packages  of  wafers  ?    How  many  pounds  ? 

14.  What  is  the  sum  of  4  2-qt.  cans  of  berries  and 
2  2-qt.  cans.     How  many  quarts  ? 

15.  Add  2  to  each  of  these  numbers: 

3,     4,     14,     24,     23,     33,     44,     13,     54 

16.  Add  4  to  each  of  these  numbers: 

1,     2,     12,     22,     31,     42,     51,     61,     82 

17.  Add  3  to  each  of  these  numbers: 

1,     2,     3,    12,     21,    23,     31,    43,    52 

18.  5  +  1=?  5+?=  6  l+?=6 
4+  ?  =  6                 2+?=  6  3+?=  6 


30  ARITHMETIC 

19.  Subtract:* 

6  6  6  6  6  16  26 

5  1  4  2  3  12  22 

20.  A  grocer  has  6  10-lb.  sacks  of  flour,  and  sells  3. 
How  many  has  he  left  ?     How  many  Ib.  ? 

21.  A  family  bought  6  2-lb.  packages  of  oatmeal 
for  the  month,  and  used  3.     How  many  Ib.  were  left? 

22.  With  a  foot  rule  measure  points  on  the  board 
1  ft.  6  in.  apart.     Measure  the  same  distance  with  a 
yardstick  divided  into  inches.     1  ft.  6  in.  =  ?  in. 

23.  Take   two  points  on  the  blackboard  not  far 
apart.     Measure  the  distance  between  them  with  a 
foot  rule  and  then  with  a  yardstick.     Write  your 
result  thus :  1  ft.  8  in.  =  20  in.     Select  other  points, 
measure,  and  write  your  results  in  the  same  way. 

24.  Measure  different  things,  as  the  width  of  the 
table,  of  the  desk,  of  the  door,  with  a  yardstick  and 
then  with   a   foot  rule.     Write   your   results  thus: 
27  in.  =  2  ft.  3  in. 

25.  1  ft.  =  ?  in.     1  ft.  2  in.  =  ?  in.     1  ft.  4  in.  =  ?  in. 

Lesson  13 

1.  5^  +  1^=? 

2.  John  paid  5  $  for  paper  and  1  f  for  a  pen. 
How  much  did  he  pay  for  both  ? 

*  Read  5  and  1  are  6,  1  and  5  are  6.    Write  down  1  under  the 
5,  and  5  under  the  1. 


LESSON  13  31 

3.  James  paid  1  f  for  a  slate  pencil  and  25  $  for 
a  book.     How  much  did  he  pay  for  both  ?  . 

4.  If  I  paid  24  dimes  for  a  hat  and  2  dimes  for  a 
collar,  how  much  did  I  pay  for  both? 

5.  If  I  paid  5  half-dollars  for  a  pair  of  shoes  and 
1  half-dollar  for  a  hat,  how  much  did  I  pay  for  both? 

6.  Represent  this  quantity  on  the  blackboard  by 
dots,  each  2  dots  representing  1  half-dollar.     What 
will  1  dot  represent?     What  quantity  will  be  repre- 
sented by  4  dots  ? 

7.  A  boy  spent  13 1  for  a  top  and  2  f  for  a  string. 
How  much  did  he  spend  ? 

8.  4^+2^=?         4^+?=6^         22^+?=25^ 

9.  A  boy  has  6^  and  spends  2^  for  a  postage 
stamp.     How  much  has  he  left  ? 

10.  A  boy  has  6  nickels  and  buys  4  oranges  at  a 
nickel  apiece.     How  much  has  he  left? 

11.  I  buy  a  gallon  of   vinegar   for   22^.     What 
change  do  I  get  back  out  of  a  25  f  piece  ? 

12.  If  in  the  purchase  of  a  ball  a  boy  receives  3 
cents  change  from  a  25  cent  piece,  what  is  the  cost  of 
the  ball? 

13.  A  piece  of  ribbon  16  yd.  long  is  cut  into  two 
pieces  ;  one  part  is  12  yd.  long.     How  long  is  the 
other  part  ? 

13  =  ?      132  + $4  =  ?      $4  +  ?  =  136. 


32  ARITHMETIC 

15.  A  man  paid  $  12  for  an  overcoat  and  $3  for  an 
umbrella.     What  did  both  cost  him  ? 

16.  A  man  paid  |4  for  a  calf  and  $32  for  a  cow. 
What  did  he  pay  for  both? 

17.  There  were  16  marbles  in  a  ring  ;  Arthur  shot 
away  3.     How  many  were  left  in  the  ring  ? 

18.  A  man  paid  5  five-dollar  bills  for  a  suit  of 
clothes  and  1  five-dollar  bill  for  a  pair   of  shoes. 
What  did  both  cost  him? 

Lesson  14 
Copy  and  add: 

ft.  in.  ft.  to.  ft.  in. 

1.      1          2  11  12 

13  14  14 


How  do  you  add  ft.  and  in.  to  ft.  and  in.? 


2. 


3. 


ft. 

in. 

ft. 

in. 

ft. 

in. 

2 

1 

2 

3 

1 

3 

1 

5 

3 

3 

5 

2 

yd. 

ft. 

in. 

yd. 

ft. 

in. 

1 

1 

1 

1 

1 

2 

1 

1 

4 

1 

1 

3 

How  do  you  add  yd.,  ft.,  and  in.  to  yd.,  ft.,  and  in.  ? 

yd.  ft.          in.  yd.          ft.  in. 

4.          1        0        1  213 

224  213 


LESSON  14  33 

5.  A  chain  3  ft.  4  in.  long  is  joined  to  another 
chain  2  ft.  2  in.  long.     How  long  is  the  chain  formed 
from  the  two  ? 

6.  Represent  these  lengths  by  lines  of  the  given 
length.     Measure  the  line  formed  by  joining  these. 
How  many  feet  and  inches  in  this  line  ? 

7.  Add  and  memorize : 

111       212      123 
123      243      543 


Subtract  : 

8.         *2        3        3 

4 

5 

5 

5 

5 

121 

2 

4 

1 

3 

2 

9.           666 

6 

6 

15 

26 

36 

514 

2 

3 

12 

24 

32 

Copy  and  subtract: 

ft.              in. 

10.      2          5 

ft. 
4 

in. 
6 

ft. 
5 

in. 

6 

1          3 

2 

3 

3 

4 

How  do  you  subtract  ft. 

and 

in.  from 

ft. 

and  in. 

? 

ft.              in. 

11.      5          4 

ft. 
6 

in. 
6 

ft. 
4 

in. 

5 

41  34  13 

Find  the  difference  in  length  between  two  ropes, 
one  8  ft.  6  in.  long,  the  other  3  ft.  4  in. 
*  Read  1  and  1  are  2,  1  and  2  are  3. 


34  ARITHMETIC 

yd.  ft.  in.  yd.          ft.  In. 

12.          2        2        4  625 


112  314 

How  do  you  subtract  yd.,  ft.,  and  in.  from  yd.,  ft., 
and  in.? 

13.  From  a  rope  5  yd.  2  ft.  6  in.  long  a  piece  3  yd. 
2  ft.  4  in.  has  been  cut.     How  much  is  left? 

14.  Measure  the  length  of  the  rope  on  the  black- 
board or  floor.     Measure  the  length  cut  off.     Now 
measure  the  remaining  part.     How  much  is  left? 

15.  Measure  in  ft.  and  in.  the  length  of  the  table, 
and  also  the  width.     Find  their  difference. 

16.  Measure  in  ft.  and  in.,  and  write  down  the 
heights  of  different  pupils  in  the  room. 

17.  Find  the  difference  in  the  heights  of  the  tallest 
and  the  shortest  girl  in  the  class.     Of  the  tallest  and 
the  shortest  boy. 

18.  Find  the  difference  in  the  heights  of  the  tallest 
boy  and  the  tallest  girl  in  the  class. 

19.  Measure  the  heights  of  several  pupils  in  yd., 
ft.,  and  in.,  and  make  questions  about  the  sum  or 
difference  of  their  heights. 

20.  James  is  6  yr.  4  mo.  old,  and  his  sister  Mary 
2  yr.  3  mo.     James  is  how  much  older  than  Mary  ? 

21.  A  milkman  pours  3  gal.  2  qt.  of  milk  from  a 
can,  and  has  2  gal.  1  qt.  left  in  the  can.     How  much 
was  in  the  can  at  first  ? 


LESSON  15  35 

Lesson  15 
•    •••          ••*/•          •••• 

1.  What  can  each  of  these  dots  represent  ?     Read 
these  dots  from  left  to  right  and  from  right  to  left. 

Add: 

2.  1         2         3          6          5          4 
654123 


3. 

1 

1 

2 

1 

1 

1 

1 

1 

6 

16 

24 

36 

45 

56 

63 

76 

4. 

6 

6 

6 

4 

6 

6 

3 

6 

1 

11 

31 

51 

71 

91 

22 

41 

5.  What  is  the  sum  of  71  in.  and  5  in.  ? 
Arthur  can  jump  71  in.  and  James  5  in.  beyond 

Arthur.     How  far  can  James  jump  ? 

6.  2222222 
5        25        45        64        85        33        55 

7.  How  many  dollars  in  3  ten-dollar  bills  and  a 
two-dollar  bill  ? 

I  paid  3  ten-dollar  bills  and  a  two-dollar  bill  for  a 
desk,  and  a  five-dollar  bill  for  a  chair.  What  did 
both  cost  ? 

8.  5555535 
2        12        31        42        62        82        92 


36  ARITHMETIC 

9.    3434343 
4          3        14        13        24        23        34 

10.  A  lady  is  34  yr.  of  age,  and  her  husband  is 
3  yr.  older.     What  is  his  age  ? 

11.  What  numbers  added  give  7? 

12.  If  in  question  1  each  dot  represents  1  pt., 
how  many  qt.  and  pt.  are  represented  by  the  7  dots  ? 

13.  What  is  the  weight  of  4  10-lb.  sacks  of  flour 
and  3  10-lb.  sacks  ? 

How  many  cents  in  5  dimes  and  2  dimes  ? 

14.  If  a  boy  is  16  yr.  old  to-day,  when  was  he 
13  yr.  old  ? 


Add: 

15.  2 

2 

2 

2 

2 

2 

3 

13 

113 

3 

23 

223 

16.  3 

3 

3 

3 

3 

3 

4 

14 

114 

4 

34 

134 

17.  134   mi.  +  3   mi.  =  ?      3   mi.  +  134   mi.  =  ? 
134  mi.  +  ?  =  137  mi.     3  mi.  +  ?  =  137  mi. 

A  gentleman  travels  134  mi.  by  train  and  drives 
3  mi.  from  the  station  to  his  friend's  house.  How 
far  does  he  go  all  together  ? 

18.  2  2  222  2 
5          25          125          5          44          145 


LESSON   16  37 

19.    6  6  66  6  6 

1          11          111          1          81          181 


20.  5^+2^=?^       5^  +  1^=?^       5^+?  =  7^ 

21.  '  1  nickel  =  ?  f  1  nickel  1  f  =  ?  X 

1  nickel  2  ^  =  ?  ^         4  nickels  =  ?  dimes 

22.  If  I  pay  2^  more  than  a  nickel  for  a  loaf  of 
bread,  what  does  it  cost  ? 

23.  Draw  two  lines,  end  to  end,  one  5  3-in.  long, 
and  the  other  2  3-in.  long.     How  many  3-in.  in  the 
whole  line  ?     How  many  inches  ?     How  many  3-in. 
in  21  in.  ? 

Lesson  16 

1.  4  +  3  =  ?  24  +  3  =  ?  32  +  ?  =  36 

2.  A  boy  spends  4^  for  an  orange  and  3^  for  a 
lemon.     How  much  does  he  spend  ? 

3.  A  pound  of  butter  costs  24^,  and  a  pint  of 
milk  3£     What  do  both  cost? 

4.  I  bought  a  bicycle  for  $36,  and  paid  132  cash. 
How  much  did  I  then  owe  ? 

5.  Henry   has    a   25-cent  piece   and   2^.     How 
much  money  has  he  ? 

6.  A  box  is  33  in.  long.     It  is  how  many  inches 
shorter  than  a  yardstick  ? 

7.  I  gave  a  five-dollar  bill  for  a  pair  of  shoes  and 
2  orie-dollar  bills  for  a  hat,     What  did  both  cost  ? 


38  ARITHMETIC 

8.  My  milkman  left  me  3  qt.  1  pt.  of  milk,  and  I 
paid  him  in  pint  tickets.      How  many  did  I  give 
him  ?     Represent  by  dots. 

9.  What  unit  does   the  grocer  use  to  measure 
kerosene  ?     To  weigh  butter  ? 

10.  What  other  units  might  be  used  in  each  of 
these  cases?      How  does   each   of   the  latter  units 
compare  in  weight  with  each  of  the  former  ? 

11.  What   is  butter  worth   a   pound  ?     What  is 
kerosene  worth  a  gallon  ?     What  unit  measures  the 
value  of  a  pound  of  butter,  and  also  of  a  gallon  of 
kerosene  ? 

12.  Measure  a  gallon  of  water  with  a  quart  meas- 
ure.    What  number  of  quarts  did  you  get  ? 

13.  Put  1  gal.  3  qt.  of  water  into  a  pail.     Meas- 
ure this  with  a  quart  measure.     What  number  did 
you  get  ?     1  gal.  3  qt.  =  ?  qt. 

14.  Empty  5  qt.  of  water  into  a  pail.     Measure 
this  with  gallon  and  quart  measures.     5  qt.  =  ?  gal. 
?qt. 


15.  If  each  dot  represents  1  qt.,  what  do  4  dots 
represent?     What  do  these  dots  represent?     How 
many  qt.  ? 

16.  Represent  2  gal.  2  qt.  by  dots.     How  many 
qt.  ?     Represent   15    qt.  by  dots.     How  many  gal. 
and  qt.?     Make  other  questions. 


LESSON   17  39 

17.  1  gal.  =  ?  qt.  1  gal.  2  qt.  =  ?  qt. 
1  gal.  3  qt.  =  ?  qt.  6  qt.  =  ?  gal.  ?  qt. 

18.  1  yr.  =  ?  mo.  1  yr.  3  mo.  =  ?  mo. 
1  yr.  5  mo.  =  ?  mo.            14  mo.  =  ?  yr.  ?  mo. 
16  mo.  =  ?  yr.  ?  mo. 

19.  Harry  is  1  yr.  and  5  mo.  old,  Charlie  is  3  yr. 
and  7  mo.  old.     What  is  the  sum  of  their  ages  ? 

20.  Charlie  is  how  much  older  than  Harry  ? 

21.  Represent  by  dots  on  the  board  the  age  of 
Charlie   in   months,    each  dot   to   represent   1    mo. 
Mark  off  by  a  line  the  number  of  dots  representing 
Harry's  age  in  months. 

22.  1  da.  =  ?  hr.  1  da.  2  hr.  =  ?  hr. 

25  hr.  =  ?  da.  ?  hr.  27  hr.  =  ?  da.  ?  hr. 

23.  If  a  cow  gives  a  gallon  of  milk  in  the  morn- 
ing and  3  qt.  at  night,  how  many  quarts  does  she 
give  in  a  day  ? 

24.  A  baby  is  1  yr.  4  mo.  old.     How  many  months 
old  is  he  ? 

Lesson  17 


l.    Read   these   dots  in  opposite  directions,  and 
write  your  results  thus :    2  +  2  +  2  =  6. 


40 


ARITHMETIC 


2.    Add: 

2 

2* 

1 

1* 

1 

1 

2 

2 

3 

3 

1 

1 

2 

12 

2 

22 

4 

34 

3.  Count  6  dots  by  2's.     How  many  2's  ?     If  each 
dot  represents  a  pint,  how  many  quarts  are  there  ? 

4.  How  many  quarts  in  3  2-qt.  ?     How  many  days 
will  5  2-qt.  jars  of  fruit  last  a  family  that  eats  1  qt.  a 
day? 

5.  How  many  days  will  3  2-lb.  rolls  of  butter  last 
a  family  that  eats  J  Ib.  a  day  ? 

6.  Read   these   dots   in   opposite   directions,  and 
write  down  your  results. 


Add: 

7.    1 

1 

1 

1 

2 

2 

2 

2 

3 

3 

3 

3 

4 

24 

3 

43 

2 

52 

8.     1 

1 

3 

1 

2 

3 

2 

4 

1 

2 

1 

2 

13 

12 

23 

34 

62 

71 

9.    What  is  the  sum  of  32^,  l£  3^?     Of  23^,  2£ 
Of  41/,  4^,  2^?    James  spent  22  f  for  a  Reader, 

*  Add  thus  :   12,  14,  16  ;  22,  25,  26. 


LESSON    17  41 

3  ^  for  a  lead  pencil,  and  2  $  for  an  eraser.    What  did 
all  cost? 

10.  A   boy   had   52^  in   the    Penny   Savings  on 
Monday.    Tuesday  he  put  in  2  ^,  and  Wednesday  3^. 
How  much  did  he  then  have? 

11.  Copy  and  add  : 

21  ^          22^          32^          26^          30^         Uf 
12  14  311         441         631 


12.  I  paid  21^  for  a  Ib.  of  butter  and  13^  for  a 
Ib.  of  cheese.     What  was  the  cost  of  both  ? 

13.  Question  12  is  founded  on  the  first  problem  in 
number  11.    Make  similar  questions,  using  the  quan- 
tities given  in  number  11. 

14.  Copy  and  add  : 

11  15  21  20  20  22 

14  30  11  30  25  21 

22  32  33  25  31  14 

15.  Name   two  units   each  of  which  is   used  to 
measure  potatoes. 

16.  Make  questions,  using  the  following  price-list: 

Coffee  at  31  f  a  Ib. 
Baking  powder  at  22  £  a  can 
Gelatine  at  13^  a  package 
Matches  at  10  f  a  package 
Nuts  at  12^  alb. 
Canctles  at  15  f  a  Ib, 


42  ARITHMETIC 

Lesson  18 
Subtract : 

1.  23344455555 
12131241325 

2.  66666777777 
51423615243 

3.  36457764276 
02417210231 

4.  What    is    the    meaning    of    4-3  =  1?       Of 
5-2  =  3?     Of6-2  =  4?     Of7-4  =  3? 

5.  I  paid  7^  for  an  apple  and  an  orange.     The 
orange  cost  5^  ;  what  did  the  apple  cost  ? 

B 

A | C 

6.    From  A  to  C  is  6  mi.     If  it  is  4  mi.  from  A 
to  B,  how  far  is  it  from  B  to  C  ? 

Copy  and  subtract : 

7.  *35^       46^        75^       66^       57^ 

22^        24^        31  £        26^        14^ 

8.  45          56          72          43          26          77 
21          11          22          13          21          15 

9.  Write  the  second  quantity  under  the  first  and 
subtract:  65  mi.  and  23  mi.;  174  and  $33. 

*  Subtract  thus :  2  and  3  are  6,  2  and  1  are  3, 


LESSON   19  48 


10.  From  A  to  C  is  35  mi.     If  it  is  22  mi.  from 
A  to  B,  how  far  is  it  from  B  to  C  ? 

11.  A  man  pays  $42  on  a  bicycle  that  cost  $  65. 
How  much  more  will  he  have  to  pay  ? 

12.  A  man  is  57  yr.  of  age,  and  his  son  25  yr. 
How  much  older  is  the  father  than  the  son  ? 

13.  A  yard  is  36  in.     How  many  inches  are  there 
in  a  stick  that  is  11  in.  shorter  than  a  yard  ? 

14.  From  a  box  containing  72  pencils  30  have  been 
taken.     How  many  are  left  in  the  box  ? 

15.  Of  a  class  of  46  pupils  34  are  dismissed.    How 
many  remain  ? 

16.  A  boy  had  75^,  and  spent  32^  for  an  Arith- 
metic.    How  much  had  he  left? 

17.  There  are  seventy-seven  pupils  in  the  first  two 
grades  of  a  school.     If  there  are  forty-three  in  the 
first  grade,  how  many  are  in  the  second? 

Lesson  19 

1.  4  +  ?  =  6          14  +  ?    =  16  2  +  ?  =  26 
6  -  4  =  ?          16-14  =  ?            26-2  =  ? 

2.  I  buy  4  qt.  of  milk  each  morning  and  2  qt. 
each  evening.     How  much  milk  do  I  buy  a  day  ? 


44  ARITHMETIC 

3.  A  man  rides  14  mi.  and  walks  2  mi.     How 
far  does  he  travel  <? 

4.  If  22  pupils  out  of  a  class  of  26  are  present, 
how  many  are  absent  ? 

5.  If  2  in.  of  snow  fell  on  Monday  and  5  in.  on 
Tuesday,  how  much  fell  on  the  two  days  ? 

6.  A  boy  spent  16^  in  one  day.     In  the  morning 
he  spent  5^.     What  did  he  spend  in  the  afternoon? 

7.  Two  boys  have  17  marbles.     If  the  first  has 
13,  how  many  has  the  second  ? 

8.  Robert  has  a  25-cent  piece,  and  Walter  a  2-cent 
piece.    How  much  money  have  the  two  boys  ? 

9.  John  had  16^  and  spent  4^  for  an  orange. 
How  much  had  he  left  ? 

10.  The  schoolroom  thermometer  registered  63° 
and  then  rose  3°.     What  did  it  then  register  ? 

11.  What  is  the  unit  that  measures  temperature  ? 

12.  What  is  the  sum  of  four  and  twelve  ? 

13.  Find  the  cost  of  two  rugs,  one  costing  $25, 
and  the  other  $42. 

14.  How  much  more  must  I  pay  for  a  waste  paper 
basket  costing  75^,  than  for  one  costing  55^? 

15.  Draw  a  line  4  2-in.  long.     How  many  inches 
long  is  it  ?     If  a  line  is  measured  by  the  number  5 
a.ncl  tlie  unit  2-in.?  how  long  is  it?    Draw  the  line, 


LESSON  20 


45 


16.  The  weight  of  a  parcel  is  measured  by  the 
number  4  and  the  unit  3-lb.    How  many  pounds  does 
it  weigh  ? 

17.  A  line  12  in.  long  is  measured  by  the  unit 
2-in.     What  number  of  2-in.  ?     6  is  often  called  the 
ratio  of  12  in.  to  2  in. 

18.  A  line  10  in.  long  is  measured  by  the  num- 
ber 5  and  a  certain  unit.     What  is  the  unit  ?    Divide 
the  line  into  5  equal  parts,  and  measure  each  part. 

19.  Memorize : 

12  12  123  123 
32  43  543  654 
44  55  666  767 

Lesson  20 


Add: 

1. 

2  dimes 

2  dimes 

3  dimes 

1  dime 

2. 
3. 

2      " 

3      " 

3     " 

4  dimes 

10^ 

40^ 

20? 
20  1 

20^ 
30^ 

30^ 
30^ 

1  dime 

3  dimes 

3  dimes 

2  dimes 

4. 
5. 

5  dimes 

4     " 

30^ 
40  1 

10  min. 

2      " 

5     " 

20^ 

50^ 

30  min. 

wy 

50^ 

30^ 

201 

20  min. 

10  min. 

' 

10    " 

20    " 

30    « 

30    « 

46  ARITHMETIC 


6.  10  in. 

20  « 

20ft. 
20  " 

20yd. 

40  " 

40  mi. 

30  " 

7.  20  min. 
10  " 

30  hr. 
10  " 

30  da. 
30  " 

20  da. 

50  " 

8.  A  boy  takes  30  min.  to  go  on  an  errand,  and 
20  min.  to  return.     How  long  is  he  gone  ? 

9.  There  are  30  da.  in  April  and  the  same  number 
in  June.     How  many  days  in  both  months  ? 

10.    What  is  the  weight  of  two  parcels,  one  weigh- 
ing 10  lb.,  and  the  other  40  Ib.  ? 


11. 

3 

30 

3 

30 

3 

30 

2 

20 

12 

120 

22 

220 

12. 

4 

40 

4 

40 

4 

40 

2 

20 

12 

120 

22 

210 

13. 

4 

40 

4 

40 

4 

40 

3 

30 

13 

130 

23 

230 

14. 

1 

10 

100 

1 

10 

100 

1 

10 

100 

2 

20 

200 

15. 

2 

20 

200 

2 

20 

200 

8 

30 

300 

5 

50 

500 

LESSON  21  47 

Subtract : 

16.  40  40            50           50            60  70 
30  20            10           20            30  40 

17.  300             500             400             600  700 
200             400             100             200  500 

18.  I  paid  20^  for  1  Ib.  of  meat.     What  change 
did  I  get  back  out  of  a  fifty-cent  piece  ? 

19.  A  farmer  had  500  bu.  of  wheat  and  sold  300  ? 
How  many  bushels  had  he  left? 

Lesson  21 


1.  Read  these  dots  from  left  to  right  and  from 
right  to  left. 

2.  If  each  dot  represent  (a)  a  cent,  (6)  an  inch, 
(V)  a  year,  (c?)  $2,  (e)  1  2-lb.,  read  the  result  from 
right  to  left  and  from  left  to  right.     Place  these 
readings  in  columns  for  addition,  and  add. 

Add: 


3.    1 

2 

3 

4 

5 

6 

7 

6 

5 

4 

3 

2 

4.    1 

1 

1 

1 

1 

1 

7 

17 

26 

37 

47 

50 

48  ARITHMETIC 


5.    2 

2 

2 

6 

46 

56 

6.     3 

3 

3 

5 

15 

115 

7.     4 

4 

4 

4 

14 

114 

8.   Add 

and  memorize  : 

1 

1 

1 

2 

1 

1 

2 

3 

2 

4 

1      2 

3 

1 

6      5 

4 

7 

222 
64  76  86 

333 
25         125         135 

444 
124         134         144 


21  123 

35  543 

234 
644 

9.    A  boy  rode  15  mi.  and  walked  3  mi.     How  far 
did  he  travel  ? 

10.  Helen  had  50  ^  and  earned  30  t  more.     How 
much  did  she  then  have  ? 

11.  Find  the  cost  of  2  Ib.  of  sugar  at  5  ^  a  lb.,  and 
3  cakes  of  soap  at  3  $  each. 

12.  A  sack  of  flour  cost  60  ^,  and  a  pound  of  coffee 
30  f.     What  did  both  cost  ? 

13.  A  young  man  is  20  yr.  old,  and  his  father  is 
50  yr.  old.     Find  the  sum  of  their  ages. 

14.  I  paid  $87  for  a  horse  and  $  55  less  for  a  cow; 
find  the  cost  of  the  cow. 


LESSON  22 


49 


Lesson  22 


•    • 

•    •               • 

y  \  *  * 

•    •    i 

>    • 

•  • 

•    •               •/ 

•  i  •  • 

•       •       4 

»    • 

1.    Read  these   dots 
and  write  your  results 
thus: 

in  opposite  directions,        2 
in  columns  for  addition, 

Ju 

2 

Add: 

8 

2. 

2             2 

3             3 

2 

2 

3              3 

3             3 

2 

2 

3           23 

2           12 

4 

44 

3. 

4             2 

2             3 

2 

1 

2             4 

3             3 

3 

1 

22            22 

33           52 

22 

45 

4.   What  is  the  meaning  of  22  +  4  +  2  =  28?     Of 
33  +  2  +  3=  38? 


5.    Read  these   dots   in   opposite   directions,  and 
write  your  results  in  columns  for  addition. 


Add: 
6.       2 
5 


23321 

61154 

21  2  42  32  53 


50  ARITHMETIC 

7.  1  5  3  1  2  1 
513243 

22  22  41  65  72  84 

8.  Count  8  dots  by  twos.     How  many  twos  ?     If 
each  dot   represents  a  pint,  how  many  quarts   are 
there  ? 

Count  by  fours.  How  many  fours  ?  If  each  dot 
represents  a  quart,  how  many  gallons  are  there  ? 

9.  If  each  of  the  8  dots  represent  $  1,  how  many 
two-dollar  bills  are  represented?     If  each  dot  repre- 
sents half-a-dollar,  how  many  dollars  are  there  ? 

10.  Count  8  dots  by  twos.  How  many  twos  ?  If 
a  family  buys  2  qt.  of  milk  a  day,  how  many  quarts 
will  it  use  in  4  days  ? 

Copy  and  add: 


11.  43 

23 

25 

42 

66 

16 

41 

51 

43 

25 

21 

71 

12.  325 

123 

404 

260 

152 

203 

132 

261 

162 

427 

233 

642 

13.  10  23  31  22  31  11 
22            21            14            10            30  21 
13            22            23            35            17            36 

14.  Make  groups  of  eight  dots  and  draw  lines  as 
in  question  1.     Write  as  many  different  columns  for 
addition  as  you  can. 


LESSON  23  51 

15.  What  two  numbers  give  8  when  added  ? 

16.  What  three  numbers  give  8  when  added  ? 

17.  I  carried  home  from  the  store  a  2-lb.  can  of 
corn,  4  Ib.  of  nuts,  and  a  2-lb.  roll  of  butter.     How 
many  pounds  did  my  parcel   weigh?      How  many 
2-lb.  ?     How  many  4-lb.  ? 

18.  The  cost  of  a  chair  is  measured  by  the  number 
5  and  the  unit  $  2.     What  is  its  cost  ? 

19.  A  debt  of  |10  is  measured  by  the  unit  $5  and 
a  certain  number.     What  is  the  number  ? 

Lesson  23 


1.  How  long  is  this  oblong  ?     How  wide  ? 

2.  Draw  a  line  as  long  as  the  four  sides  of  this 
oblong.     How  long  is  it?     The  perimeter   of   this 
oblong  is  8  in. 

3.  Draw  an  oblong  2  in.  long  and  1  in.  wide. 
What  is  the  length  of  its  perimeter  ? 

4.  Draw  a   square   each  side  of   which  is  2  in. 
What  is  the  length  of  its  perimeter? 


ARITHMETIC 


5.  Draw  a  square  each  side  of  which  is  1  inch. 
This  is  called  a  square  inch.     Draw  a  square  each 
side  of  which  is  4  inches.     How  many  square  inches 
in  this  square  ?     How  many  4-sq.  in.  ?     What  units 
of  measurement  are  used  in  the  measurement  of  this 
4-inch  square  ? 

6.  How  long  is  this  oblong?     How  wide?     It 
contains  3  square  inches  (3  sq.  in.).     One  square 
inch  is  the  unit  that  measures  the  area  of  the  oblong. 

7.  Draw  an  oblong  4  in.  long  and  1  in.  wide. 
Divide  it  into  square  inches.     What  is  its  area? 

8.  What  is  the  area  of  an  oblong  5  in.  long  and 
1  in.  wide  ?    6  in.  long  and  1  in.  wide  ? 

9.  Draw  an  oblong  containing  8  sq.  in.      How 
many  2-sq.  in.  does  it  contain  ?     How  many  4-sq.  in.? 


Add: 

hr. 

10.   3 

2 


min. 

2 
4 


hr.          min. 

4        20 
3        30 


hr. 

5 
1 


min. 

4 

22 


LESSON  24 


53 


da. 

11.    2 
5 


hr. 

5 
3 


da. 

20 
40 


hr. 
1 


yr. 

3 


da. 
30 

30 


12.  A  boy  is  8  yr.  6  mo.  old,  and  his  sister  5  yr. 
2  mo.     What  is  the  difference  between  their  ages  ? 

13.  A  table  is  3  ft.  6  in.  long  and  2  ft.  6  in.  wide. 
What  is  the  sum  of  the  length  and  width?     What 
is  the  perimeter  of  the  table  ? 


Lesson  24 


1.  Read  these  dots  from  left  to  right  and  from 
right  to  left. 

2.  Make  two  groups  of  9  dots  each.     Draw  lines 
and  show  that 

9  ==  8  +  1,  or  1  +  8 ;    7  +  2,  or  2  +  7. 


Add: 

3. 

1 

1 

1 

1 

1 

3 

1   1 

1 

8 

18 

26 

38 

48 

53 

68  70 

88 

4. 

2 

2 

2 

2 

2 

2 

2 

2 

7 

17 

117 

125 

137 

147 

153 

167 

3 

3 

3 

3 

3 

3 

3 

3 

6 

16 

113 

216 

316 

326 

335 

346 

54  ARITHMETIC 

5.  A  man  paid  $  65  for  a  bicycle,  and  spent  $  4  in 
repairs  during  the  year.     What  was  the  entire  cost? 

6.  454545          45 
5415142524        35        34 

7.  Memorize : 

9  =  8  +  1,  or  1  +  8 ;    7  +  2,  or  2  +  7 ; 
6  +  3,   or   3  +  6 ;     5  +  4,   or  4  +  5. 

8.  Arrange  9  dots  in  groups  of  3.     How  many  3 
dots  in  9  dots?     If  each  dot  represents  a  foot,  what 
unit  of  length  do  3  dots  represent  ? 

9.  If  each  dot  represents  1  Ib.  of  lard,  how  many 
3-lb.  pails  of  lard  are  represented  by  9  dots  ? 

10.  Add  3  to  each  of  the  following  numbers : 
6,   16,    26,    36,   46,   56,    66,   76,    86,    96. 

11.  I  paid  $  35  for  a  sofa,  the  price  of  which  had 
been  reduced  $  4.     What  was  the  original  price  ? 

12.  Subtract  4  from  each  of  the  following  num- 
bers: 

9,   19,   29,   39,   49,   59,   69,   79,   89,   99. 

13.  I  paid  $  49  for  a  rug,  less  $  5  for  cash.     What 
did  the  rug  cost  ? 

14.  Copy  and  add  : 

25    27    32    40    36    54    16    60 
34    42    51    46    63    24    53    19 


LESSON  25  55 

15.  Copy  and  subtract  : 

76         92         48         78         63         76         59         99 
23         81         34         37         12         26         41         64 

16.  A  debt  is  measured  by  the  number  5  and  the 
unit  $2.     What  is  the   debt?     With  the  unit  1  5, 
what  number  would  measure  the  debt? 

Lesson  25 

=  ?     7  +  ?  =  9 
=  9     4  +  ?  =  9 


i. 

8 

+ 

1  =  ? 

8 

+  ? 

=  9 

7 

+  ^ 

2. 

6 

+ 

?  =  9 

3 

+  ? 

=  9 

5 

+  1 

3. 

Subtract  : 

9 

8 

6 

9 

9 

7 

9 

6 

3 

4 

2 

1 

2 

7 

896 
450 

4.  Bertha  is  4  yr.  old,  and  her  sister  9.     In  how 
many  years  will  Bertha  be  as  old  as  her  sister  is 
now? 

5.  A  post  9  ft.  long  is  3  ft.  below  ground.     How 
long  is  the  part  above  ground  ?     Draw  this  post. 

6.  Write    the    following    numbers    under    each 
other,  and  add:   12  and  36  ;   25  and  51  ;  42  and  27  ; 
33  and  53. 

7.  A  boy  is  12  yr.  old,  and  his  father  36.     What 
is  the  sum  of  their  ages  ? 

8.  It  took  me  26  min.  to  ride  4  mi.  on  a  bicycle 
against  the  wind,  and  21  min.   to  return  with  the 
wind.     How  long  was  I  gone  and  how  far  did  I  ride  ? 


56  AEITHMETIC 

9.    There  are  28  da.  in  Feb.  and  31  da.  in  March. 
How  many  days  are  there  in  the  two  months  ? 

10.  Write  the  following  numbers  under  each  other, 
and  subtract  the  smaller  from  the  larger  :   86  and 
64  ;  78  and  31 ;  18  and  89  ;  95  and  34. 

11.  A  boy  has  earned  $ 32  toward  buying  a  1 55 
bicycle.     How  much  has  he  still  to  earn  ? 

12.  Albert  has  75  ^,  and  his  sister  Florence  50  ^. 
Albert  has  how  much  more  than  Florence  ? 

Lesson  26 


Subtract  : 

1. 

5 

15 

25 

6 

16 

26 

6 

26 

3 

3 

3 

2 

2 

2 

3 

3 

2. 

7 

27 

6 

36 

8 

48 

9 

49 

5 

5 

4 

4 

3 

~3 

7 

~7 

3. 

8 

58 

7 

37  ' 

9 

29 

9 

19 

6 

6 

4 

~4 

2 

~2 

4 

~4 

4.  A  person  having  a  25  ^  piece  buys  two  2  $  post- 
age stamps.     What  change  does  he  get  in  return  ? 

5.  Out  of  18  baskets  of  plums   3   baskets   are 
spoiled.     How  many  are  good? 

6.  It  took  me  19  min.  to  row  a  certain  distance 
up  stream,  and  6  min.  less  to  return.     How  long  did 
it  take  to  return  ? 


LESSON  26 


57 


7.  Read  these  dots  from  left  to  right  and  from 
right  to  left,  and  write  your  results  in  columns  for 
addition. 

8.  If  each  dot  represents  $  1,  what  unit  of  money 
will  5  dots  represent  ?   2  dots  ?     How  many  dollars  in 
a  five-dollar  bill  and  2  two-dollar  bills  ? 

9.  If  each  dot  represents  1  ft.,  what  unit  does  a 
group  of  3  dots  represent  ?     What  is  the  sum  of  2  ft., 
1  yd.,  and  4  ft.  ? 

10.  Make  9  dots  in  groups  of  3  dots.     How  many 
3's  in  9?     Three  yd.  of  tape  at  3^  a  yd.,  find  the  cost. 
Paid  $  9  for  3  bbl.  of  apples.     Find  cost  per  bbl. 

11.  Arrange  9  dots  in  groups  of  2's.     Let  each  dot 
represent  1  pt.     Make  two  questions.     Arrange  in 
groups  of  4's.     Let  each  dot  represent  1  qt.     Make 
two  questions. 

12.  Make  groups  of  9  dots  and  draw  lines  as  in 
question  7.     Write  as  many  different  columns  for 
addition  as  you  can. 


Add: 
13.     1 

5 
3 


14. 


3 
3 

63 


1 

5 

13 

2 

2 

42 


2 
3 

22 

2 

5 

31 


5 

3 

31 

4 

3 

12 


1 
6 

72 


2 
3 

83 


1  2 

3  5 

64  72 


58  ARITHMETIC 

15.  Three  years  ago  I  was  32  years  old.     How  old 
shall  I  be  4  years  from  now? 

16.  I  paid  |61  for  a  bicycle,  $2  for  a  lamp,  and  $6 
for  a  bicycle  suit.     What  was  the  entire  cost  ? 

Lesson  27 

1.  Copy  and  add : 

123  203  216  14  201  464 
212  231  101  301  462  301 
333  543  672  484  125  213 

2.  Copy  and  subtract : 

762  968  650  934  687  989 
421  265  120  323  534  232 

3.  Write    the    following    numbers    under   each 
other  and  add :    323  and  462 ;    236  and  423 ;    683 
and  214  ;  337  and  542. 

4.  Write    the    following    numbers    under   each 
other   and   subtract   the   smaller   from   the   larger  : 
697  and  182 ;  265  and  495 ;  108  and  279 ;  848  and 
316. 

5.  I  pay  $250  for  a  span  of  horses  and  $220  for 
a  carriage.     Find  the  cost  of  both. 

6.  There  are  255  pupils  in  the  grammar  school 
and  41  in  the  high  school.     How  many  pupils  are 
there  in  the  entire  school? 


LESSON  28  59 

7.  There  are  35  pupils  in  the  first  grade,  32  in 
the  second,  and  30  in  the  third.     How  many  pupils 
are  there  in  the  first  three  grades  ? 

8.  There  are  48  pupils  in  the  Kindergarten,  of 
whom  26  are  between  5  and  6  years  old.     How  many 
are  between  4  and  5  ? 

9.  Of  a  school  of  255  pupils,  231  were  present 
on  Friday.     How  many  were  absent  ? 

10.    If  I  read  122  pages  of  a  book  containing  346 
pages,  how  many  will  I  have  still  to  read  ? 

Lesson  28 


1.  Read  these  dots  from  left  to  right  and  from 
right  to  left. 

2.  Count  10  by  5's.     How  many  5's  in  10  ?     How 
many  nickels  in  a  dime?     Count  10  by  2's.     How 
many  2's  in  10?     How  many  1 2  in  $10? 

3.  If  each  dot  represents  a  nickel,  what  unit  of 
money  will  5  dots  represent  ?     What  unit,  if  each  dot 
represents  1  dime ?   $1?   1 2? 

4.  Arrange  10  dots  in  groups  of  2,  3,  and  4,  and- 
let  each  dot  represent  1  pt.,  1  ft.,   or  1  qt.     Make 
questions  similar  to  Lesson  16,  questions  16  and  17. 


60  ARITHMETIC 

5.   If  $10  is  counted  by  a  $2  unit,  what  is  the 
number?     5  is  often  called  the  ratio  of  810  to 


6.  Make  three  groups  of  10  dots  each.     Draw 
lines  and  show  that 

10  =  9  +  1  or  1  +  9;    8  +  2  or  2  +  8  ;    6  +  4  or  4  +6. 

7.  Name  the  number  which  added  to  each  of  the 
following  numbers  gives  10  : 

8,     5,     3,    1,     7,    4,     9,    2,    0,     6,    10. 

8.  Fill  the  blanks  : 

6  +  ?  =  10        5  +  ?  =  10        2  +  ?  =  10       7  +  ?  =  10 

9.  Add:    22334455 

818172726364555 

10.    What  unit  of  money  is  equal  to  10^?     5^? 
100^? 


11.  If  I  buy  two  2  ^  postage  stamps,  how  much 
change  shall  I  get  back  out  of  a  dime? 

12.  If  I  buy  a  postal  card,  how  much  change  will 
I  get  back  out  of  a  dime  ?     Out  of  a  half-dollar  ? 

13.  Some  boys  spent  45  ^  for  melons  and  5  $  for 
peaches.     How  much  did  they  spend  ?     What  unit 
of  money  would  pay  for  both  ? 

14.  A  farmer  sows  16  A.  with  wheat  and  3  A.  with 
oats.     How  many  acres  did  he  sow  ? 

15.  A  man  is  27  yr.  old,  and  his  son  3  yr.     What 
is  the  sum  of  their  ages  ?     What  is  the  difference  ? 


LESSON  29  61 

16.    Two  boys  hire  a  boat  one  hour  for  20  ^.     If 
the  first  pays  15  ^,  what  does  the  second  pay  ? 


Lesson  29 


1.  Read  these  dots  from  left  to  right  and  from 
right  to  left,  and  write  your  results  in  columns  for 
addition. 

2.  Make  groups  of  10  dots  and  draw  lines  as  in 
question  1.     Write  as  many  different  columns  for 
addition  as  you  can. 


Add: 

3.    2 

4 

4 

5 

1 

3 

3 

2 

2 

3 

3 

4 

5 

4 

24 

42 

66 

83 

4.    4 

2 

12 


2 

4 

33 


1 

3 

56 


2 
3 

72 


5  3 

1  3 

94          102 


5.  Copy  and  add: 

231                222  212  102  202 

321                134  303  214  471 

215                541  584  683  416 


6.    Find  the  sum  of  1142,  $  225,  and  1 312. 


62  ARITHMETIC 

7.  Subtract: 

10          9          10          8          10          9          10          10 
~62~51~24~1~3 

8.  Copy  and  subtract: 

942   .  896  107  1085  1077 


611  703  63  823  562 

9.    On  a  debt  of  $685  I  pay  $435.     How  much 
do  I  still  owe  ? 

10.  Write  the  following  numbers  under  each  other 
and  add: 

21,  60,  and  15  ;    42,  27,  and  30  ;    333,  324,  and  511. 

11.  Write    the    following    numbers    under    each 
other  and  subtract  the  smaller  from  the  larger: 

899  and  473  ;  1064  and  521 ;  1056  and  823. 

12.  I  bought  three  bicycles,  paying  for  the  first 
$40,  for  the   second   $22,  and  for  the  third  $16. 
What  did  I  pay  for  all  three  ? 

13.  James  weighs  107  lb.,  and  George  82  Ib.    How 
much  more  does  James  weigh  than  George  ? 

14.  I  paid  10  $  for  bread,  32  ^  for  coffee,  and  56  ^ 
for  butter.     What  did  I  pay  for  all  ? 

15.  A  farmer   planted  12  cherry  trees,    24   apple 
trees,  and  13  plum  trees.     If  eleven  died,  how  many 
trees  were  there  in  his  orchard? 


1.    Add: 


SECTION   III 
Lesson  30 


$2 

$2 

2 

12 

2 

2 

$2 

2 

2 

2 

$2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2.  What  is  the  sum  of  the  last  column  ?     Count 
the  number  of  $  2  in  the  last  column.      6  x  1 2  =  1 12. 

3.  2xf2  =  ?    3x12  =  ?    4xf2  =  ?    5x$2=? 

4.  If  1  hat  costs  |2,  what  will  6  hats  cost? 


5.  Count  these  dots  by  2's.     How  many  2's  in  6  ? 
Count  by  3's.     How  many  3's  in  6  ? 

6  =  3x2  or  2x3. 

6.  If  each  dot  represents  a  pint,  how  many  repre- 
sent a  quart?     How  many  quarts  in  6  pt. ?     What 
will  6  pt.  of  syrup  cost  at  2  dimes  a  quart? 

7.  If  each  dot  represents  1^,  how  many  represent 
the  value  of  a  2^  postage  stamp  ?    What  will  3  2-cent 
postage  stamps  cost? 


£4  ARITHMETIC 

8.  If  each  dot  represents  1  ft.,  what  unit  will  3 
dots  represent?     How  many  feet  in   2  yd.?     What 
will  6  ft.  of  tape  cost  at  3^  a  yd.? 

9.  3x2dimes  =  ?  2  x  3  dimes  =  ? 
3x2  tens  =  ?  tens  2x3  tens  =  ?  tens 
3x2  5-lb.  =  ?  5-lb.             2x3  5-lb.  =  ?  5-lb. 

10.  What  is  the  cost  of  3  yd.  of  ribbon  at  2  dimes 
a  yd.  ?  How  many  ten  yard  lengths  of  carpet  in  3 
times  2  ten  yard  lengths  ? 


11.  Count  8  dots  by  2  dots  ;  8^  by  2^;  8  dimes  by 
2  dimes  ;  8  3-lb.  by  2  3-lb.  ;  8  2-yd.  by  2  2-yd.  ;  8  6-sq. 
in.  by  2  6-sq.  in.    How  many  2's  in  each  case  ?    How 
many  2-units  in  an  8-unit  quantity? 

12.  Count   again   by   4's.     How  many  4   dots  in 
8  dots?   4^  in  8^?   4  dimes  in  8  dimes?   4  3-lb.  in  8 
3-lb.?   4  2-yd.  in  8  2-yd.?   4  6-sq.  in.  in  8  6-sq.  in.? 
How  many  4-units  in  an  8-unit  quantity  ? 

13.  How  many  2's  in  8?     How  many  4's  in  8? 

8  =  4x2  or  2x4. 

14.  Place  10  dots,  count  by  2's  and  5's,  and  show 

that 

10  =  5  x  2  or  2x5. 

Count  again  as  in  questions  11  and  12. 

15.  Place  12  dots  so  as  to  show  that 

12  =  6  x  2  or  2  x  6. 


LESSON  30  65 

16.  Place  14,  16,  18,  20  dots,  and  make  similar 
questions. 

17.  Memorize  : 

6  =  2x3  or  3x2. 

8  =  2x4  or  4x2. 

10  =  2  x  5  or  5  x  2. 

12  =  2  x  6  or  6  x  2. 

18.  2  and  3  are  called  factors  of  6.     What  are  the 
factors  of  8?  10?  12714?  16?  18?  20? 

19.  2  is  one  factor  of  18.     What  is  the  other? 
How  many  2^  stamps  can  you  buy  for  18^? 

20.  How  many  2-lb.  bricks  of  codfish  weigh  24  Ib.  ? 

21.  A  board  12  ft.  long  is  cut  into  4  pieces.     Find 
length  of  each  piece.     If  cut  into  4  ft.  pieces,  how 
many  pieces  ? 

22.  What  is   the  total   weight  of   5  2-lb.  cans  of 
peas,  2  3-lb.  cans  of  tomatoes,  2  6-lb.  boxes  of  starch, 
andl  10-lb.  sack  of  flour? 

23.  Vegetables  are  put  up  in  1,  2,  and  3-lb.  cans, 
and  flour  in  10-lb.  sacks.     Using  this,  make  examples 
like  question  22. 

24.  Name  the  even  numbers  from  2  to  12.     What 
number  is  a  factor  of  all  these  even  numbers  ?    Name 
all  the  odd  numbers  from  1  to  11.     Is  2  a  factor  of 
these  ?     How  can  you  change  an  odd  number  to  an 
even  number? 


ARITHMETIC 

Lesson  31 


1. 

2  x  1  in.  =  ? 

2  x  5  in.  =  ? 

2  x    9  in. 

=  ? 

2  x  2  in.  =  ? 

2  x  6  in.  =  ? 

2  x  10  in. 

9 

2  x  3  in.  =  ? 

2  x  7  in.  =  ? 

2  x  11  in. 

=  ? 

2  x  4  in.  =  ? 

2  x  8  in.  =  ? 

2  x  12  in. 

9 

2. 

3x2ft.=  ? 

3  x  2  yd.  =  ? 

3x2  mi. 

=  ? 

2x3ft.  =  ? 

2x3yd.  =  ? 

2x3  mi. 

=  ? 

3. 

3x    $2  =  ? 

3x$20=? 

3x$200 

_  9 

2x   $3  =  ? 

2x$30  =  ? 

2x$300 

=  ? 

4. 

4x   $2  =  ? 

4x$20  =  ? 

4x$200 

—  ? 

2x   $4  =  ? 

2x$40  =  ? 

2  x  $400 

=  ? 

5.  A  dealer  sold  4  sets  of  furniture  at  $200  each, 
and  2  bookcases  at  $30  each.     What  did  all  sell  for? 

6.  A  farmer  received  $200  for  a  span  of  horses, 
$20  apiece  for  3  cows,  and  $4  apiece  for  2  sheep. 
What  did  he  receive  all  together? 

7.  4x$20  =  ?  5x820  =  ?  6x   $20  =  ? 
2x$40  =  ?            2x$50=?  2x   $60  =  ? 

8.  7x$20  =  ?  8x$20  =  ?  9x   $20  =  ? 
2x$70  =  ?            2x$80  =  ?           2x 


9.    10x$20  =  ?          llx$20  =  ?          12  x   $20  =  ? 
20x$10  =  ?          20x$ll  =  ?         20  x   $12  =  ? 


LESSON  31 


67 


10.  What  is  the  cost  of  3  2-lb.  rolls  of  butter  at 
a  lb.,  2  Ib.  of  coffee  at  30^  a  lb.,  and  2  cakes  of 

soap  at  4  ^  a  cake  ? 

11.  Find  the  cost  of  2  lb.  meat  at  12  ^  a  lb.,  1  can 
corn  at  13^,  1  doz.  lemons  at  30^  a  doz.,  and  1  lb. 
bacon  at  12^  a  lb. 

Copy  and  multiply : 

12.     22^          22^          22^          21^         21^          21^ 
234567 


13.  123 
2 


143 
2 


134 
2 


154 
2 


182 
2 


14.  Place   2  under  each  of  these  quantities,  and 
multiply:  24  £  $42,  13  lb.,  52  mi.,  30  da.,  64  yr. 

15.  There  are  24  hr.  in  1  da.     How  many  hours  in 
2  da.? 

16.  If  there  are  21  hills  of  potatoes  in  a  row,  how 
many  hills  are  there  in  6  rows  ? 

17.  Multiply  23  lb.  by  2,  and  21  lb.  by  3.     Add 
your  results. 

18.  What  is  the  cost  of  5  doz.  eggs  at  21^  a  dozen, 
and  2  lb.  of  tea  at  42^  a  pound? 

19.  Memorize : 

Two  times 


Iis2 

5  is  10 

9  is  18 

2  is  4 

6  is  12 

10  is  20 

3  is  6 

7  is  14 

11  is  22 

4  is  8 

8  is  16 

12  is  24 

68  ARITHMETIC 

20.  What   is   the   meaning   of    2  x  3  =  6  ?      Of 

4x2  =  8? 

21.  Place  dots  so  as  to  show  that  the  factors  of  14 
are  2  and  7  or  7  and  2.     How  many  pounds  of  rice 
at  7^  a  pound  can  you  buy  for  14^? 

22.  How  many  8-lb.  pails  of  butter  can  you  get 
from  16  lb.?     From  160  lb.? 

23.  A  length  of  24  ft.  is  measured  by  the  unit 
4  ft.,  what  is  the  number  ?    Draw  this  length,  making 
1  in.  for  1  ft.,  and  measure,  counting  the  number. 
If  the  number  is  4,  what  is  the  unit  of  measure  ? 

24.  What  are  the  factors  of  16  (16  =  2  x  8  or  8 

x  2),  18,  20,  22,  24  ? 

Lesson  32 

1.  1  qt.  =  ?  pt.          8  qt.  =  ?  pt.          10  qt.  =  ?  pt. 
3  qt.  =  ?  pt.          5  qt.  =  ?  pt.          12  qt.  =  ?  pt. 

6  qt.  =  ?  pt.          9  qt.  =  ?  pt.          11  qt.  =  ?  pt. 

2.  How  many  times  must  a  pint  measure  full  of 
water  be  emptied  into  a  quart  measure  to  fill  it? 
By  what  number  must  you  multiply  to  reduce  quarts 
to  pints?     A  pint  is  what  part  of  a  quart? 

3.  A  pitcher  holds  3  qt.  of  milk.     How  many 
pints  will  it  hold? 

4.  2  qt.  1  pt.  =  ?  pt.  6  qt.  1  pt.  =  ?  pt. 
3  qt.  1  pt.  =  ?  pt.                    10  qt.  1  pt.  =  ?  pt. 

7  qt.  1  pt.  =  ?  pt.  12  qt.  1  pt.  =  ?  pt. 


LESSON  32  69 

5.  How  do  you  reduce  8  qt.  and  1  pt.  to  pints? 
Multiply  the  number  of  quarts  by  2,  and  add  1  to 
get  the  number  of  pints. 

6.  lof    6in.  =  ?in.  £  of  18  in.  =  ?  in. 
l  of  10  in.  =  ?  in.  1  of  24  in.  =  ?  in. 
J  of  14  in.  =  ?  in.                     J  of  16  in.  =  ?  in. 

7.  lof|4  =  ?        £  off  40  =  ?         lof  |400  =  ? 

8.  i  of    6  pt.  =  ?  pt.  J  of  16  pt.  =  ?  pt. 
l  of    8  pt.  =  ?  pt.  i  of  22  pt.  =  ?  pt. 
1  of  12  pt.  =  ?  pt.                    1  of  18  pt.  =  ?  pt. 

9.  2  pt.  =  1  qt.          6  pt.  =  ?  qt.        20  pt.  =  ?  qt. 
4  pt.  =  ?  qt.        12  pt.  =  ?  qt.        24  pt.  =  ?  qt. 

10.  5  pt.  =  ?  qt.  ?  pt.         15  pt.  =  ?  qt.  ?  pt. 
9  pt.  =  ?  qt.  ?  pt.         23  pt.  =  ?  qt.  ?  pt. 

11.  What  will  8  yd.  of  silk  cost  at  1 2  a  yd.? 

12.  If  a  boy  rides  9  mi.  an  hour,  how  far  will  he 
ride  in  2  hr.? 

13.  What  will  5  qt.  1  pt.  of  milk  cost  at  2^  a  pt.  ? 

14.  What  will  4  pt.  of  milk  cost  at  6/  a  qt.  ? 

15.  What  is  the  price  of  2  qt.  1  pt.  of  milk  at  6^  a 
quart  ? 

16.  There  are  29  fruit  trees  in  an  orchard,  5  are 
cherry  trees,  4  plum,  and  the  rest  apple ;  how  many 
apple  trees  are  there? 


TO 


ARITHMETIC 

Lesson  33 


1.  How  long  is  this  oblong  ?     How  wide  ? 

2.  How  many  square  inches  does  it  contain  ? 

3.  The  unit  of  length  used  to  measure  short  dis- 
tances is  1  in.     The  unit  of  area  used  to  measure 
small  areas  is  1  square  inch  (1  sq.  in.). 

4.  Draw  an  oblong  4  in.  long  and  1  in.  wide,  and 
divide  it  into  sq.  in.     What  is  its  area  ? 

5.  Draw  an  oblong  6  in.  long  and  1  in.  wide,  and 
divide  it  into  sq.  in.     What  is  its  area  ? 

6.  What  is  the  area  of  an  oblong  8  in.  long  and 
1  in.  wide  ?    10  in.  long  ?    12  in.  long  ? 

7.  Make  an   oblong  4  in.  long   and  2  in.  wide. 
Divide  it  into  sq.  in.     How  many  sq.  in.?     Count 
by  4's.     How  many  4  sq.  in.  ?     Count  by  2's.     How 
many  2  sq.  in.  ? 

8.  Make   an   oblong  8  in.  long  and  2  in.  wide. 
Divide  it  into  sq.  in.      How  many  sq.  in.?     Count 
by  8's.     How  many  8  sq.  in.  ?     Count  by  2's.     How 
many  2  sq.  in.  ? 


LESSON    33  71 

9.    Make  other  oblongs,  divide  them  into  sq.  in., 
and  count  their  areas  by  sq.  in.,  2  sq.  in.,  and  so  on. 


10.  How  long  is  this  oblong  ?     How  wide  ? 

11.  Into  how  many  rows  is  it  divided  ?     What  is 
the  area  of   each  row?     What  is  the  area  of  the 
oblong  ? 

12.  The  area  of  this  oblong  is  measured  by  the 
number  6  (2  x  3)  and  the  unit  1  sq.  in. 

13.  Make  an  oblong  4  in.  long  and  2  in.  wide. 
Divide  it  as  the  oblong  in  question  7  is  divided. 

14.  What  number  measures  its  area  ?     What  is  its 
area? 

15.  What  number  measures  the  area  of  an  oblong 
5  in.  long  and  2  in.  wide  ?     What  is  its  area  ? 

16.  What  is  the  area  of  an  oblong  6  in.  long  and 
2  in.  wide  ? 


72  ARITHMETIC 

17.  How  do  you  find  the  number  of  sq.  in.  in  an 
oblong  3  in.  long  and  2  in.  wide?     4  in.  long  and 
2  in.  wide  ?     6  in.  long  and  2  in.  wide  ?     8  in.  long 
and  2  in.  wide?     10  in.  long  and  2  in.  wide?     Any 
length  and  any  width  ? 

18.  Make  problems  like  questions  15  and  16. 

Lesson  34 

1.2x3  =  6.     2  and  3  are  called  factors  of  6.    6 
is  the  product  of  2  and  3. 

2.  2  and  4  are  the  factors  of  what  number  ?     4 
and  2  are  the  factors  of  what  number  ? 

3.  2  and  6  are  the  factors  of  what  number?     2 
and  7?     9  and  2?     2  and  11  ?     12  and  2? 

4.  2  is  one  factor  of  8.    What  is  the  other  factor  ? 
4  is  one  factor  of  8.     What  is  the  other  factor  ? 

5.  2  is  one  factor  of  each  of  the  following  num- 
bers, what  is  the  other  factor  ?     12,  18,  24,  16,  6,  14, 
10,  22. 

6.  7  is  one  factor  of  14.   What  is  the  other  factor  ? 
9  is  one  factor  of  18.     What  is  the  other  factor  ? 

7.  What  are  the  factors  of  each  of  the  following 
numbers :  6,  10,  12,  8,  20,  16,  24,  14,  22  ? 

8.  If  1  yd.  of  silk  costs  $3,  what  will  2  yd.  cost  ? 

9.  If  2  is  one  factor  of  10,  what  is  the  other  fac- 
tor?   If  2  loaves  of  bread  cost  10^,  what  will  1 
loaf  cost? 


LESSON  35  73 

10.  If  a  man  walks  1  mi.  in  20  min.,  how  long 
will  he  take  to  walk  4  mi.  ? 

11.  If  1  horse  costs  1200,  what  will  4  such  horses 
cost? 

12.  What  must  8^  be  multiplied  by  to  give  16^? 
At  8^  a  pound,  how  many  pounds  of  rice  will  cost 
16/2 

13.  What  will  2  doz.  lead  pencils  cost  at  24  $  a 
dozen? 

14.  What  will  5  boxes  of  note  paper  cost  at  20^  a 
box? 

Lesson  35 

1.  2x    3^=    6£      iof    6^  =  ?          6^-    3^  =  ? 
2x    6^  = 

2x    9^  = 
2x12^  =  24^. 

2.  What  is  the  meaning  of  J  of  8  =  4?     Of  |  of 
12  =  6? 


3.  |-of|16  =  ?  l  of  |160  =  ?  iof24mi.  =  ? 
l  of  240  mi.  =?  l  of  6  in.  =?  \  of  8  ft.  =  ? 

4.  1  ft.  =  12  in.  1  ft.  =  ?  in.  2  ft.  =  ?  in. 

5.  1  dime  =  10  ^  1  dime  =  ?  ^.  2  J-  dimes  =  ?  ^ 

6.  11  =  100^.  »£  =  ?£  I2i=?^. 

7.  1  doz.  =  12.  1  doz.  =  ?  21  doz.  =  ? 

8.  1  hr,  =  60  min.  J  hr.  =  ?  min.  2J  hr.  =  ?  mill, 


74  ARITHMETIC 

9.    1  da.  =  24  hr.        J-  da.  =  ?  hr.        |  yr.  =  ?  mo. 

10.  1  gal.  =  4  qt.         1  gal.  =  ?  qt.       2 J-  gal.  =  ?  qt. 

11.  1  qt.  =  2  pt.  6 J  qt.  =  ?  pt.       10  qt.  =  ?  pt. 

12.  If  1  gal.  of  kerosene  costs  1  dime,  what  part 
of  a  dime  will  J  gal.  cost  ?     How  many  cents  will 
^  gal.  cost  ? 

13.  If  1  Ib.  of   sugar  costs  6^,  how  many  cents 
will  21  Ib.  cost  ? 

14.  What  will  half-a-dozen  lemons  cost  at  24  $  a 
doz.?  Half-a-doz.  silver  spoons  at  $  22  a  doz.  ?   1^  doz.  ? 

15.  A  pail  contains  8  qt.  of  water.     How  many 
quarts  will  be  left  in  the  pail  after  10  pt.  are  taken 
out? 

16.  If  1  qt.  of  molasses  costs  40  ^,  what  will  1  pt. 
cost?     What  will  2  qt.  1  pt.  cost? 

17.  A  dish  holds  3  qt.  of  berries  and  1  pint  more. 
How  many  pints  did  it  hold,  and  what  did  they  cost 
at  10^  a  qt.? 

18.  How  many  quarts  in  2  gal.  2  qt.  ?     How  many 
pints  in  2  gal.  2  qt.  1  pt.  ?     In  1  gal.  3  qt.  1  pt.  ? 

19.  What  is  the  cost  of  2  gal.  2  qt.  1  pt.  of  milk 
at  2  f  a  pt.  ? 

What  does  a  milkman  gain  by  buying  1  gal.  3  qt. 
1  pt.  of  milk  at  2  f  a  pt.  and  selling  it  at  3  ^  a  pt.  ? 

20.  Copy  and  multiply : 

21^  32^  44^  53^  64^  72^ 

2  2  2-2  2  2 


LESSON   36  75 

21.  How  much  more  will  2  yd.  of  cloth  cost  at 
44?  a  yd.  than  3  yd.  at  22^  a  yd.  ? 

22.  A  boy  walks  2  mi.  to  the  depot,  rides  on  the 
train  for  2  hr.  at  the  rate  of  32  mi.  an  hour,  and  then 
drives  4   mi.  to   his   friend's   house.     What   is   the 
whole  distance  ? 

23.  Make  questions  using  the  following  price  list  : 
Coffee  at  30^  a  Ib.  Butter  at  24^  a  Ib. 
Eggs  at  14  ^  a  doz.  Fruit  at  22  ^  a  qt. 

Lesson  36 


1.  How  long  is  the  line  a  ?     How  long  is  the 
line  b? 

2.  Compare  b  with  a.     The  line  b  is  measured  2 
times  by  the  line  a.     The  ratio  of  b  to  a  is  2. 

3.  Compare  a  with  b.     What  part  of  b  is  needed 
to  make  a  ?     a  is     of  b.     The  ratio  of  a  to  b  is    . 


4.  How  long  is  a  ?     How  long  is  b  ? 

5.  Compare  b  with  a.     b  is  measured  how  many 
times  by  a  ?     The  ratio  of  5  to  a  is  what  ? 

6.  Compare  a  with  5.     What  part  of  b  needed  to 
make  a  ?     The  ratio  of  a  to  £  is  what  ? 


76  ARITHMETIC 

7.  Compare    4   in.    with   2  in.      A    4-in.  line   is 
measured  how  often  by  a  2-in.  line  ?     The  ratio  of 
4  in.  to  2  in.  is  2. 

8.  Compare  2  in.  with  4  in.     What  part  of  4  in. 
is  needed  to  make  up  2  in.  ?     2  in.  is  |  of  4  in.    The 
ratio  of  2  in.  to  4  in.  is  J. 

9.  Draw  a  line  3  in.  long.     Draw  a  line  6  in, 
long.     Divide  this  line  into  parts  each  3  in.  long. 

10    Compare  6  in.  with  3  in.     3  in.  measures  6  in, 
how  many  times  ?     The  ratio  of  6  in.  to  3  in.  is  2. 

11.  Compare  3  in.  with  6  in.     What  part  of  6  in. 
is  needed  to  make  up  3  in.  ?     3  in.  is  what  part  of  6 
in.  ?     The  ratio  of  3  in.  to  6  in.  is  what? 

12.  Memorize  :    J  is  the  ratio  of  1  in.  to  2  in. ; 
of  2  in.  to  4  in.  ;  of  3  in.  to  6  in. 

Lesson  37 

Copy  and  add  : 


1. 

2 

1 

2 

3 

2 

2 

4 

6 

3 

3 

2 

3 

1 

6 

4 

1 

2 

4 

4 

3 

5 

2 

1 

3 

2. 

2 

3 

3 

5 

3 

2 

4 

2 

6 

1 

4 

1 

22 

33 

40 

51 

62 

73 

3. 

4 

6 

3 

1 

4 

3 

1 

2 

3 

3 

3 

3 

10 

81 

43 

61 

12 

92 

LESSON   37  77 


21 

12 

54 

66 

73 

24 

11 

30 

21 

10 

14 

30 

51 

46 

34 

22 

12 

25 

231 

111 

121 

545 

32  1 

222 

304 

502 

123 

130 

314 

182 

375 

331 

533 

6.  There  are  102  pages  in  the  First  Reader,  150 
in  the  Second,  and  245  in  the  Third.  How  many 
pages  are  there  in  the  three  Readers  ? 

Copy  and  subtract : 

32  45  64  96  85  69 

'   11  31  22  73  32  26 

245  329  675  486  1065 

123  115  254  232  253 

9.  A  man's  salary  is  $840,  in  addition  to  which 
he  has  an  income  of  $245.  If  his  yearly  expenses 
are  $  625,  how  much  can  he  save  ? 

896  678  795  888  999 

'   273  207  385  543  601 

2345  3546  6547          9861          7209 

1223  2314  4236  2341  2106 

12.    A   span   of   horses   weighs    2469   Ib.     If   one 
weighs  1224  Ib.,  what  does  the  other  weigh  ? 


78  ARITHMETIC 

Copy  and  multiply  : 

13.   232  j*          423  j*          634^          804  j*          806  <* 

2  2  2  2.2 


14.  Make  simple  practical    questions   illustrating 

$8  -=-  2  =  |4,  and  $8  -i-  $2  =  4.     What  is  the  mean- 
ing of  6  H-  2  =  3  ? 

Copy  and  divide  : 

15.  2)42       2)84       2)66       2)28       2)46       2)88 

16.  2)246        2)128        2)642        2)804        2)188 

17.  |636 -3  =  ?      $488 -s- $4  =  ?      $168-*- 8  =  ? 

18.  If  a  2-lb  roll  of  butter  costs  64  £  what  is  the 
price  per  Ib.  ? 

19.  What  is  the  price  of  cheese  per  Ib.  when  4  Ib. 

cost  84^? 

20.  Out  of  a  bag  containing  159  nuts  4  children 
each  took  a  handful  and  there  were  still  left  in  the 
bag  119   nuts.     How  many  nuts   did   the   children 
take  ?     How  many  did  each  get  on  the  average  ? 

Lesson  38 

1.  Draw  a  line  1  ft.  long.     Draw  a  line  2  ft. 
long.     Divide  this  line  into  parts  each  1  ft.  long. 

2.  Compare  2  ft.  with  1  ft.     The  ratio  of  2  ft. 
to  1  ft.  is  what  ? 


LESSON  38  79 

3.  Compare  1  ft.  with  2  ft.     What  part  of  2  it. 
is  needed  to  make  up  1  ft.  ?     1  ft.  is  what  part  of  2 
ft.?     The  ratio  of  1  ft.  to  2  ft.  is  what  ? 

4.  What  is  the  ratio  of  1  yd.  to  2  yd.?     Of  1^ 
to  2^?     Of  $1  to  $2?     Of  1  da.  to   2   da.?     Of 
1  hr.  to  2  hr.  ? 

5.  If  1 2  will  buy  12  yd.  of  ribbon,  what  part  of 
12  yd.  will  $  1  buy  ?     How  many  yards  ? 

6.  If  a  train  travels  60  mi.  in  2  hr.,  what  is  the 
rate  per  hour  ? 

7.  Draw  a  line  4  in.  long.     Draw  a  line  8  in. 
long.     Divide  this  line  into  parts  each  4  in.  long. 

8.  Compare  8  in.  with  4  in.     8  in.  is  measured 
how  many  times  by  4  in.?     The  ratio  of  8  in.  to 
4  in.  is  what  number  ? 

9.  What  is  the  ratio  of  8  ft.  to  4  ft.  ?    Of  8^ 
to  4^?     Of  $8  to  $4?     Of  8  da.  to  4  da.?     Of 
8  hr.  to  4  hr. 

10.  A  boy  walks  10  mi.  in  4  hr.     At  the  same 
rate,  how  many  times  10  mi.  will  he  walk  in  8  hr.  ? 
How  many  miles  ? 

11.  If  $4  buys  3  yd.  of  cloth,  how  many  yards 

will  1 8  buy? 

12.  Compare  4  in.  with  8  in.     What  part  of  8  in. 
is  needed  to  make  up  4  in.  ?     4  in.  is  what  part  of 
8  in.  ?     What  is  the  ratio  of  4  in.  to  8  in.  ? 


gO  ARITHMETIC 

13.  What  is  the  ratio  of  4  ft.  to  8  ft.  ?     Of  $4 
to  18?     Of  4  yr.  to  8  yr.  ?     Of  4  Ib.  to  8  lb.? 

14.  At  the  rate  of  18  a  doz.,  what  part  of  a  dozen 
pairs  of  stockings  will  cost  $4?     How  many  pairs? 
What  will  4  bars  of  soap  cost,  at  the  rate  of  8  for 


15.  Draw  lines  5  in.  long  and  10  in.  long.     Divide 
the  line  10  in.  long  into  parts  each  5  in.  long. 

16.  What  is  the  ratio  of   10   in.   to  5  in.?     Of 
5  in.  to  10  in.? 

17.  What  is  the  ratio  of  2  to  4?     3  to  6?     4  to  8? 
5  to  10? 

18.  Name  other  numbers  that  J  is  the  ratio  of. 

19.  2  is  the  ratio  of  what  numbers  ? 

20.  What  is  the  ratio  of  12  to  6  ?     Of  6  to  12  ? 
Of  16  to  8  ?    Of  8  to  16  ? 

21.  What  will  8  lb.  of  sugar  cost,  when  16  lb.  are 
sold  for  84^  ?     What  will  12  lb.  cost  ? 

22.  What  is  the  ratio  of  1  qt.  to  1  pt.?     Of  1  pt. 
to  1  qt.?    Of  1  dime  to  1  nickel?    Of  1  nickel  to  1 
dime  ?    Of  one  -quarter  dollar  to  one-half  dollar  ? 

Lesson  39 

1.  The  length  of  a  sheet  of  drawing-paper  is  9  in. 
Here  the  unit  of  measure  is  1  in.  The  number  that 
measures  the  length  is  9. 


LESSON  39  81 

2.  The  width  of  a  sheet  of  drawing-paper  is  6  in. 
What  is  the  unit  of  measure?     What  is  the  number 
that  measures  the  width  ? 

3.  The  length  of  a  table  is  4  ft.     What  is  the 
unit  of  measure  ?     What  is  the  number  that  measures 
its  length  ?    4  is  the  ratio  of  the  length  to  1  ft. 

4.  The  width  of  a  room  is  6  yd.     What  is  the 
unit  of  measure  ?     What  is  the  number  ? 

5.  The    distance   between   two   cities   is  30  mi. 
What  is  the  unit  of  measure  ?     What  is  the  number 
of  units  ? 

6.  A  pitcher  holds  3  qt.  of  milk.     What  is  the 
unit  of  measure  ?     What  number  measures  the  quan- 
tity of  milk  ? 

7.  A  pail  holds  6  2-qt.  cans  of  milk.     What  is 
the  unit  of  measure  ?     What  is  the  number  of  units  ? 
How  many  gallons  will  the  pail  hold  ? 

8.  The  quantity  of  kerosene  in  a  can  is  measured 
by  the  number  5  and  the  unit  of  measure  1  gal.     How 
much  kerosene  is  there  in  the  can  ? 

9.  I  buy  10  bu.  of  potatoes.     What  is  the  unit  ? 
What  number  measures  the  quantity  of  potatoes  ? 

10.  A  family  eats  2  5-lb.  pails  of  butter  in  1  mo. 
What  is  the  unit  ?  How  many  units  of  1  Ib.  each.  ? 
How  many  2-lb  rolls  of  butter  would  the  family  eat 
in  one  month  ? 


82  ARITHMETIC 

11.  When  a  grocer  sells  sugar,  why  does  he  weigh 
it  ?     What  unit  does  he  use  ? 

12.  A  book  contains  250  pages.     What  number 
measures  the  size  of  the  book  ?     What  is  the  unit  ? 

13.  A  room  is  8  yd.  1  ft.  6  in.  long.     What  three 
units  are  used  to  measure  the  length  of  the  room  ? 

14.  The  quantity  of  berries  in  a  crate  is  measured 
by  the  number  16  and  the  unit  1  qt.     How  many 
quarts  of  berries  are  there  in  a  crate  ? 

15.  The  cost  of  a  yard  of  ribbon  is  measured  by 
the  number  2  and  the  unit  1  dime.     How  many  cents 
did  it  cost  ?   What  is  the  ratio  of  the  cost  to  1  nickel? 

16.  If  the  unit  of  money  is  a  ten-dollar  bill,  how 
many  dollars  are  there  in  2  units  ? .   If  there  are  2 
units  of  money  in  20  ^,  what  is  the  unit  ?     Paid  an 
account  of  1 50  with  5  coins  of  equal  value.     How 
many  dollar  units  is  each  coin  worth  ? 

17.  Draw  two  oblongs  each  of  which  will  contain 
6  sq.  in. 

18.  An  oblong  contains  6  sq.  in.     What  is  the 
unit  of  measure  ?     What  number  measures  the  area  ? 
With  a  2-sq.  in.  unit,  what  number  ?     With  a  3-sq. 
in.  unit,  what  number  ? 

Lesson  40 

1.    What  is  the  ratio  of  1  in.  to  2  in.  ?    Of  1 
1  ft.  to  2  ft.  ?     Of  1  yd.  to  2  yd.  ?      - 


LESSON   40  83 

2.  If  2  yd.  of  cloth  cost  $1,  what  part  of  $1 
will  1  yd.  cost.  ?     How  many  cents  ? 

3.  If  2  yd.  of  ribbon  cost  12  £  what  part  of  12^ 
will  1  yd.  cost.?     How  many  cents? 

4.  What  is  the  ratio  of   2  Ib.   to  4  Ib.  ?      If  4 
Ib.  of  sugar  cost  20^,  what  part  of  20^  will  2  Ib. 
cost.  ?     What  will  2  Ib.  cost  ? 

5.  If  4  loaves  of  bread  cost  24^,  what  part  of 
24^  will  2  loaves  cost  ?     What  will  2  loaves  cost  ? 

6.  What  is  the  ratio  of  4  to  2  ?     If  2  lead  pen- 
cils cost  5^,  what  will  4  lead  pencils  cost  ? 

7.  What  is  the  ratio  of   3  to  6?     If    6   spools 
of  thread  cost  22^,  what  part  of  22^  will  3  spools 
cost  ?     What  will  3  spools  cost  ? 

8.  What  is  the  ratio  of  8  to  4  ?     If  4.  lemons 
costs  10^,  how  many  times  10^  will  8  lemons  costs? 
What  will  8  lemons  cost  ? 

9.  What  is  the  ratio   of   a   nickel   to  a  dime  ? 
If  a  dime  will  buy  12   bananas,  how  many  will  a 
nickel  buy  ? 

10.  What   is   the  ratio   of   4   Ib.    to   2   Ib.  ?      If 
2  Ib.  of  coffee  cost  70^,  how  many  times  70^  will 
4  Ib.  cost  ?     What  will  4  Ib.  cost  ? 

11.  What  is  the  ratio  of  a  50^  piece  to  a 
piece?     Of  a  25^  piece  to  a  50^  piece? 


84 


ARITHMETIC 


12.  If  a  50^  piece  will  buy  16  Ib.  of  walnuts,  how 
many  pounds  will  a  25  $  piece  buy  ? 

13.  What  is  the  ratio  of  1  unit  of  any  kind  (as  2 
Ib.,  3  yd.,  or  $4)  to  two  units  of  the  same  kind  (as  4 
Ib.,  6  yd.,  or  $8)  ?     If  2  units  of  ribbon  (as  6  yd.) 
cost  80^,  what  will  1  unit  (or  3  yd.)  cost? 

14.  Draw  an  oblong  3  in.  long  and  2  in.  wide. 
Draw  an  oblong  3  in.  long  and  1  in.  wide.     What 
is  the  ratio  of  the  first  oblong  to  the  second  ? 


Lesson  41 

1.    Memorize  : 

Three  times 

lis    3 

5  is  15 

9  is  27 

2  is    6 

6  is  18 

10  is  30 

3  is    9 

7  is  21 

11  is  33 

4-is  12 

8  is  24 

12  is  36 

2.  Count  by  3's  from  3  to  36. 

3.  Count  by  3's  from  36  to  3. 


4.    Count  the  number  of  these  dots  by  4's ;  by  3's. 
There  are  how  many  counts  of  4  dots  ? 
There  are  how  many  counts  of  3  dots  ? 
12  =  3  x  4  or  4  x  3. 


LESSON  41  85 

5.  If  each  dot  represents  1  ft.,  what  do  3  dots 
represent?     How  many  yards  in  12  ft.?     How  many 
feet  in  8  yd.  2  ft.  ? 

6.  If  each  dot  represents  1  qt.,  how  many  dots 
represent   1   gal.?      How   many    quarts   in    3   gal.? 
What  is  the  price  of  3  gal.  2  qt.  of  kerosene  at  12^ 
per  gal.  ? 

7.  If  each  dot  represents  1  sq.  in.,  draw  the  figure 
represented  by  the  12  dots?     How  long  is  it?     How 
wide  ?     What  is  the  area  of  an  oblong  4  in.  long  and 
3  in.  wide?     4  yd.  long  and  3  yd.  wide?     Draw  a 
square  yard  on  the  blackboard. 

8.  Place  15  dots  so  as  to  show  that 

15  =  3  x  5  or  5  x  3. 

How  many  feet  in  5  yd.?     The  area  of  an  oblong 
5  in.  long  is  15  sq.  in.     How  wide  is  it? 

9.  3  is  one  factor  of  each  of  the  following  num- 
bers, what  is  the  other  :    6,  18,  12,  21,  30,  24,  36,  27, 
33? 

10.  9  is  one  factor  of   18.      What    is    the   other 
factor  ?     8  is  one  factor  of  24  ?     What  is  the  other 
factor  ? 

11.  What  are  the  two  factors  of  each  of  the  fol- 
lowing numbers : 

21  (3  x  7  or  7  x  3),  12,  27,  9,  33,  18,  36,  15,  30? 

12.  12  is  one  factor  of  36,  what  is  the  other?    How 
many  feet  in  36  in.  ?     A  dozen  yards  of  cloth  cost  36 
dimes,  what  is  the  cost  of  1  yd.  ?     How  many  cents  ? 


86  ARITHMETIC 

Copy  and  multiply : 


13. 

21 

33 

42 

63 

52 

13 

3 

3 

3 

3 

3 

r. 

14. 

72 

53 

81 

92 

60 

82 

3 

3 

3 

3 

3 

• 

15. 

112 

221 

321 

231 

333 

20;} 

3 

3 

3 

3 

3 

3 

16. 

7 

3    5 

3 

3 

3    3 

3 

3 

7    3 

5 

9 

6    8 

12 

17. 

30 

31 

32 

31 

34 

31 

5 

7 

4 

9 

2 

5 

18.  Find  the  total  cost  of  : 

3  Ib.  crackers  at  7  f  a  Ib. 

2  Ib.  wafers  at  12^  a  Ib. 
7  Ib.  oatmeal  at  3  1  a  Ib. 

3  Ib.  of  raisins  at  10^  a  Ib. 

19.  A  man  walked  east.  3  lir.  at  the  rate  of  3  mi. 
an  hr.,  and  then  walked  west  5  mi.     How  far  was  he 
then  from  his  starting-point?     Draw  a  line  to  repre- 
sent the  road,  and  mark  the  distances. 

20.  3)39     3)63     3)96     3)246     3)336     3)696 

21.  5)105    6)186     7)140    8)248    9)279    9)189 


22.   How  many  weeks  are  there  in  210  da.  ?     How 
many  gallons  in  128  qt.  ?     How  many  yd.  in  150  ft.? 


LESSON  42  87 

23.  A  man  walks  12  mi.  at  the  rate  of  3  mi.  an 
hr.,  and  returns  at  the  rate  of  4  mi.  an  hour.     How 
many  hours  is  he  gone  ? 

24.  A  farmer  divides  336  A.  equally  among  his  3 
sons.     What  is  the  share  of  each? 

Lesson  42 


Multiply  : 

1. 

4 

40 

50 

200 

30 

30 

110 

3 

3 

3 

3 

6 

8 

3 

2. 

60 

30 

120 

80 

30 

700 

300 

3 

9 

3 

3 

5 

3 

4 

3.  A  milkman  traded  3  horses  worth  $  80  each  for 
7  cows  worth  $30  each.     How  much  money  should 
he  receive  in  addition  ? 

4.  2ft.  =  ?in.    2ft.  6in.  =  ?in.    3  ft.  2  in.  =  ?in. 

5.  24  in.  =  ?  ft.  28  in.  =  ?  ft.?  in. 

39  in.  =  ?ft.?in. 

6.  1  gal.  =  4  qt.  3  gal.  2  qt.  =  ?  qt. 

3  gal.  3  qt.  =  ?  qt. 

7.  6yd.  =  ?ft.     6yd.  2ft.  =  ?ft.     8  yd.  1  ft.  =?ft. 
How  do  you  reduce  yards  to  feet? 

8.  12  ft.  =? yd.    8ft.=?yd.?ft.    28  ft.  =  ? yd.? ft. 
How  do  you  reduce  feet  to  yards  ? 


88  ARITHMETIC 

9.    17  ft.  =  ?  yd.  ?  ft.         23  ft.  =  ?  yd.  ?  ft. 
34ft.  =  ?yd.  ?ft. 

10.  A  jug  contains  3  gal.  2  qt.  of  cider.     How 
many  quarts  of  cider  are  there  in  the  jug? 

11.  A  room  is  6  yd.  2  ft.  long.     How  many  feet 
long  is  it  ? 

12.  A  rope  is  15  ft.  long.    Into  how  many  pieces 
each  1  yd.  long  can  it  be  cut  ? 

13.  From  a  piece  of  cloth  4  yd.  long  a  piece  2  ft. 
long  has  been  cut.     How  many  feet  of  cloth  are  left? 

14.  If  1  qt.  of  milk  costs  6  ^,  find  the  cost  of  1  qt. 
and  1  pt.     Of  2  qt.  and  1  pt. 

15.  If  1  yd.  of  cambric  costs  12^,  find  the  cost  of 
2  yd.  1  ft.     Of  3  yd.  1  ft. 

16.  What  will  a  man  earn  in,  1  wk.  3  da.  at  $3 
a  day. 

17.  If  a  boy  picks  8  pt.  of  berries  in  1  hr.,  how 
many  quarts  will  he  pick  in  3  hr.  ? 

18.  My  chicken  coop  is  3  yd.  1  ft.  long  and  2  yd. 
wide.     How  long  must  a  rope  be  to  go  around  it  ? 

19.  If  my  hens  lay  6  eggs  a  day,  how  many  dozen 
do  they  lay  in  one  week  ?     What  are  they  worth  at 
20  f  a  doz.  ? 

20.  I  divide  ^  of  24  ^  equally  among  3  boys.     What 
does  each  get?     ^  of  24  is  3  times  what  number? 
J  of  16  is  4  times  what  number?     J  of  42  is  3  times 
what  number  ? 


LESSON  43 

Lesson  43 


89 


1.  What  is  the  length  of  this  oblong?     What  is 
its  width?     How  many  square  inches  are  there  in 
the  first  row  ?     How  many  rows  ?     The  area  =  3  x 
3  sq.  in.  =  9  sq.  in. 

2.  Draw  an  oblong  4  in.  long  and  3  in.  wide. 
Divide  it  as  the  oblong  in  question  1.     What  is  its 
area? 

3.  Represent  the  area  of  the  oblong  in  question  2 
by  dots,  putting  one  dot  for  each  square  inch. 


90  ARITHMETIC 

4.  What  is  the  area  of  an  oblong  6  in.  long  and 
3  in.  wide  ?     8  in.  long  and  3  in.  wide  ? 

5.  Make  examples  like  question  3. 

6.  Draw  on  the  board  an  oblong  3  ft.  long  and 

2  ft.  wide.     What  is  its  area  ?     Draw  a  square  yard. 
How  many  square  feet  in  its  area  ? 

7.  What  is  the  area  of  an  oblong  4  ft.  long  and 

3  ft.  wide  ?    6  ft.  long  and  3  ft.  wide  ?    6  yd.  long 
and  3  yd.  wide  ? 

8.  Draw  the  last  oblong  in  question  6,  making 
1  in.  for  1  yd.     What  doBS  1  sq.  in.  in  your  drawing 
represent  ? 

9.  An  oblong  contains  12  sq.  in.     The  unit  of 
measure  is  1  sq.  in.     The  number  12  measures  the 
area. 

10.  What   number   and  what   unit   measure   the 
area  of  an  oblong  containing  8  sq.  in.  ?     16  sq.  in.  ? 
6  sq.  ft.  ?     10  sq.  ft.  ?     9  sq.  yd.  ?     14  sq.  yd.  ? 

11.  An  oblong  is  4  in.  long  and  3  in.  wide.     What 
number  measures  its  area  ?     What  is  its  area  ? 

12.  An  oblong  is  8  in.  long  and  3  in.  wide.    What 
number  measures  its  area  ? 

13.  What  numbers  measure  the  areas  of  the  fol- 
lowing oblongs,  and  what  are  their  areas  ? 

Length  Width  Length  Width 

4  in.  2  in.  10  in.  3  in. 

6  in.  2  in.  7ft.  3ft. 

9  in.  3  in.  8  yd.  3  yd. 


LESSON  44  91 

14.  A  room  is  12  ft.  long  and  9  ft.  wide.     How 
many  square  yards  of  carpet  are  needed  to  cover  it? 

15.  One   oblong   is    7  in.   long  and  2  in.   wide. 
Another  is  5  in.  long  and  3  in.   wide.      Which  is 
larger,  and  how  much  ? 

16.  A  rug  is  bought  for  a  room  15  ft.  by  12  ft. 
If  the  edge  of  the  rug  is  everywhere  1  ft.  from  the 
wall,  what  are  its  length  and  breadth?     Draw  the 
room  and  rug  on  the  board,  making  1  in.  for  1  ft. 

Lesson  44 

1.  What  will  8  lemons  cost  at  3^  each? 

2.  What  will  3J  yd.  of  ribbon  cost  at  8^  a  yd.  ? 

3.  What  is  the  cost  of  12  yd.  of  tape  at  2J^  a  yd.  ? 

4.  If  3  bbl.  of  flour  cost  $18,  what  will  1  bbl. 
cost? 

5.  What  is  the  cost  of  one  dozen  oranges  at  3^ 
apiece  ? 

6.  A  man  walks  3  mi.  an  hour  for  6  hr.     How 
far  does  he  walk  ?    How  long  is  he  gone  if  he  returns 
at  the  rate  of  9  mi.  an  hr.  ? 

7.  A  man  travels  6  hr.  at  the  rate  of  30  mi.  an 
hour.     How  far  does  he  travel  ? 

8.  How  many  days  are  there  in  3  wk.  2  da.  ? 

9.  How  many  hours  will  it  take  to  drive  24  nii., 
at  the  rate  of  8  mi.  an  hour  ? 


92  ARITHMETIC 

10.  If  a  bag  holds  3  bu.  of  potatoes,  how  many 
bags  will  hold  36  bu.  ? 

11.  Place  3  under  each  of   these  quantities  and 
multiply :  $  22,  31^,  42  qt.,  52  Ib. 

12.  Find  the  cost  of  3  bicycles  at  $  32  apiece. 

13.  A  milkman  has  92  customers  who  take  on  the 
average    3  qt.  of  milk  a  day.     How  many  quarts  of 
milk  does  he  sell  a  day? 

14.  Divide  each  of  these  quantities  by  3 :    $  60, 
39^,  66  qt.,  93  Ib.,  216  bu. 

15.  If  3  bu.  contain  96  qt.,  how  many  quarts  are 
there  in  1  bu.  ? 

16.  In  how  many  weeks  will  a  person  pay  $156 
for  board  at  the  rate  of  $  3  a  week  ? 

17.  If  1  boy  can  do  a  piece  of  work  in  6  da.,  how 
long  will  it  take  3  boys  to  do  it? 

Lesson  45 

1.  1  of    6  in.  =  ?     1  of    18  in.  =:  ?     £  of    24  in.  =  ? 
£  of  33  in.  =  ?     l  of  150  in.  =  ?     J  of  210  in.  =  ? 

2.  12  in.  -*-  3  in.  =  ?  12  in.  -=-  3  =  ? 
21  in.  -=-  3  in.  =  ?  21  in.  -f-  3  =  ? 
18  in.  ^-6  in.  =  ?  18  in.  ^  6  =  ? 

3.  1ft.    =?in.          Jft.    =?in.          J  ft.    =  ?  in. 
£  yd.  =  ?  ft.          1  yd.  =  ?  in.          £  yd.  =  ?  in. 


LESSON  45  93 

4.  1  da.    =  ?  hr.       J-  da.     =  ?  hr.       £  da.    =  ?  hr. 

1  hr.     =  ?  min.    J  hr.     =  ?  min.    ^  hr.     =  ?  rnin. 

5.  1  min.  =  ?  sec.     ^  min.  =  ?  sec.     -J  min.  =  ?  sec. 
j-  doz.  =  ?  £  doz.  =  ?         J-  doz.  +  1  doz.  =  > 

6.  If  3  Ib.  of  sugar  cost  15^,  what  will  1  Ib. 
cost?     What  will  2  Ib.  cost? 

7.  I  paid  $18  for  coal  at  16  a  ton.     How  many 
tons  did  I  buy  ? 

8.  If  3  gal.  of  kerosene  cost  36^,  what  will  1 
gal.  cost  ?     What  will  2  gal.  cost  ? 

9.  Mary  spends  24  ^  for  lace  at  12  $  a  yd.     How 
many  yards  does  she  buy  ? 

10.  Divide  2  dozen  roses  equally  among  3  persons. 

11.  A  man  buys  2  horses  for  $  220.     What  is  the 
cost  of  each  horse  ? 

12.  An  oblong  is  4  in.  long  and  3  in.  wide.     How 
many  square  inches  does  it  contain  ? 

13.  An  oblong  contains  15  sq.  in.     If  it  is  3  in. 
wide,  how  long  is  it  ?     Draw  the  oblong. 

14.  I  bought  1^  doz.  bananas  at  the  rate  of  15^  a 
doz.     What  did  I  pay  for  them  ? 

15.  A  mason  earns  30  $  an  hour.     How  much  will 
he  earn  in  1  da.,  if  he  works  9  hr.  a  day  ? 


94  ARITHMETIC 

Lesson  46 

1.  Draw  a  line  2  in.  long.      Draw  a  line  6  in. 
long.     6  in.  is  measured  how  many  times  by  2  in.  ? 
The  ratio  of  6  in.  to  2  in.  is  what  ?     The  ratio  of 
2  in.  to  6  in.  is  what  ? 

2.  Draw  lines  4  in.  and  12  in.  long.     12  in.  is 
measured  how  many  times  by  4  in.  ?     The  ratio  of 
12  in.  to  4  in.  is  what? 

3.  The  ratio  of  12  apples  to  4  apples  is  what  ? 
If  4   apples   cost  5^,  how  many  times   5^  will  12 
apples  cost  ?     What  will  12  apples  cost  ? 

4.  What  is  the  ratio  of  15  in.  to  5  in.?     What  is 
the  ratio  of  5  in.  to  15  in.? 

5.  What  is  the  ratio  of  18  in.  to  6  in.?     What  is 
the  ratio  of  6  in.  to  18  in.? 

6.  What  is  the  ratio  of  6  to  2  ?    2  to  6  ?    8  to  4? 
4  to  8  ?    15  to  5  ?    5  to  15  ?    18  to  6  ?    6  to  18  ? 

7.  What  is  the  ratio  of  5  ft.  to  15  ft.?   18  Ib.  to 
61b.?   18  doz.  to  6  doz.?   $8  to  $24? 

8.  If  15  Ib.  of  butter  cost  13,  what  will  5  Ib. 
cost? 

If  5  yd.  of  silk  cost  $  8,  how  many  yards  will  cost 
$24? 

9.  l  is  the  ratio  of  4  to  ?     5  to  ?     6  to  ?     7  to  ? 
8  to  ?     9  to  ?     10  to  ?     11  to  ?    12  to  ? 

10.    3  is  the  ratio  of  12  to  ?    15  to  ?     18  to  ?     21 
to  ?     24  to  ?     27  to  ?     30  to  ?     33  to  ?     36  to  ? 


LESSON  47  95 

11.  ^  is  the  ratio  of  what  numbers  ?     3  is  the  ratio 
of  what  numbers  ? 

12.  What  is  the  ratio  of  6  doz.  to  18  doz.?     If  18 
doz.  eggs  cost  1 3,  what  will  6  doz.  cost  ? 

13.  What  is  the  ratio  of  1  yd.  to  1  ft.?     If  1  ft.  of 
ribbon  cost  5^,  what  will  1  yd.  cost? 

14.  What  is  the  ratio  of  1  ft.  to  1  yd.?     If  1  yd. 
of  lace  costs  30^,  what  will  1  ft.  cost? 

15.  What  is  the  ratio  of  8  wk.  to  24  wk.?     If  I 
pay  8120  for  board  for  24  wk.,  what  part  of  1120 
must  I  pay  for  8  wk.?     What  must  I  pay  for  board 
for  8  wk.? 

16.  What  is  J  the  ratio  of  ?     What  is  2  the  ratio 
of? 

17.  The  ratio  of  the  value  of  a  purse  to  its  con- 
tents is   |.     If   the  purse  is  worth  $3,  how   much 
money  does  it  contain  ? 

Lesson  47 

1.  Jof$60=?        lof|48=?        Jof$63=? 
1  of     88  =?        J  of     39  =?        -l  of     99  =? 

2.  Draw  a  line    1    ft.  long,  and  divide  it  into 
halves.     How  many  halves  are  there  in  1  ft.? 

1  ft.  =  |  ft.     (Read,  1  ft.  =  2  halves  of  a  foot.) 

3.  11  ft.  =  |  ft.         2  ft.  =  2  ft.         21  ft.  ==  2  ft- 

41  ft.  =  2   ft'  6  -ft-  =  2   ft'  7i  ft'  =  2   ft' 

How  do  you  reduce  5J  ft.  to  halves  of  a  foot  ? 


96  ARITHMETIC 

4.  |  ft.  =  ?  ft.  |  ft.  =  ?  ft.  |  ft.  =  ?  ft. 

f  ft.  =  ?  ft.  |  ft.  =  ?  ft.          ^L  ft.  =  ?  ft. 

5.  1  qt.  =  ?  pt.         £  qt.  =  ?  pt.        41  qt.  =  ?  pt. 
6J  qt.  =  ?  pt.        8J  qt.  =  ?  pt.      121  qt.  =  ?  pt. 

How  do  you  reduce  5  J  qt.  to  pints  ? 

6.  1  pt.  =  ?  qt.          4  pt.  =  ?  qt.          5  pt.  =  ?  qt. 
9  pt.  =  ?  qt.        15  pt.  =  ?  qt.        21  pt.  =  ?  qt. 

How  do  you  reduce  7  pt.  to  quarts  ? 

7.  What  is  the  cost  of  5  pt.  of  milk  at  6  ^  a  qt.  ? 

8.  3    +  21  =  ?          11  +  2    =  ?         21  +    l  =  ? 
41  -f-  11  =  ?         51  +  31  =  ?         81  +  21  =  ? 

9.  What  is  the  weight  of  a  parcel  containing  1^- 
Ib.  of  ham  and  2 J  Ib.  of  steak  ? 

Add: 


10.  $21 

H 

14 
§ 

131 
« 

$41 
6 

$21 
12 

fioi 

101 

11.   21 
^ 

% 
12J 

% 
221 

B| 

^ 

H 

24^ 

4 

44J 

12.  211 

14 

13.  221 
2321 

32| 
331 

45 
441 

3151 
4231 

311 

561 

6041 
314 

181 
M| 

2301 
4251 

46| 
5^ 

3561 
42l| 

2431 
5121 

14.    I  paid  $21  for  a  hat  and  $5  for  a  coat.    What 
change  should  I  get  back  out  of  a  ten-dollar  bill? 


LESSON  47  97 

15.  What  is  the  price  of   two  rugs,  one   costing 
$121  and  the  other  $161? 

16.  3    +  11  =  ?  3    +  ?  =  41  .   J  +  ?  =  1 

31  +  2|  =  ?  3-1  +  ?  =  6  41  +  ?  =  8 

17.  James  is  6  yr.  old,  and  his  brother  4J.     What 
is  the  difference  in  their  ages  ? 

Subtract : 

is  §i        M        Ii        I.        !L        1<L 

"  4  5  21  21  41  61 


19    37J          581          85i  43-1          64  58 

'  24  13  611  201          221          3(51 

2Q    6261        3491        567          2161        475          7031 
504          1291        4241        204          4441        6021 

21.  What  is  the  difference  in  price  between  two 
china  closets,  one  of  which  costs  $  52J  and  the  other 

$32? 

22.  I  select  the  cheaper  of  two  bookcases,  one  of 
which  costs  $77^  and  the  other  $621.      With   the 
difference  in  price  how  many  chairs  can  I  buy  at  $5 
apiece  ? 


SECTION  IV 

Lesson  48 

1.  Count  by  4's  from  4  to  48. 

2.  Count  by  4's  from  48  to  4. 

3.  Memorize  : 

Four  times 


lis    4 

5  is  20 

9  is  36 

2  is    8 

6  is  24 

10  is  40 

3  is  12 

7  is  28 

11  is  44 

4  is  16 

8  is  32 

12  is  48 

4.  Give    two    factors   of   each   of    the    following 
numbers  :  12,  28,  36,  8,  44,  32,  48,  24,  20,  16,  40. 

5.  5  is  one  factor  of  15,  what  is  the  other  ?    5  apples 
cost  15  ^,  what  will  3  cost  ? 

6.  5  is  a  factor  of  15  tens,  what  is  the  other  ?    3  is 
a  factor  of  15  tens,  what  is  the  other  ? 

At  3  dimes  a  dozen,  how  many  dozen  oranges  can 
you  buy  for  12  dimes?     How  many  oranges? 

Multiply  : 

7.  21^       32^       $52       $41       72  mi.       81  mi. 

44444  4 


LESSON  48  99 

8.  321    434    233    523    312    422 

2    _2    _3    _3    _j±    _4 

9.  What   is  the  cost  of   4  doz.   eggs  at  21^  a 
dozen,  and  6  bunches  of  celery  at  the  rate  of  3  for 


10.  What  is  the  cost  of  4  Ib.  of  coffee  at  32^  a  lb., 
and  i  lb.  of  tea  at  60^  per  lb.  ? 

11.  An  express  train  runs  42  mi.  an  hour.     How 
far  does  it  go  in  4  hr.  ?     How  much  farther  than  a 
train  that  runs  at  half  the  rate  ? 


12. 

6 

4 

4 

4 

4 

4 

4 

4 

4 

6 

8 

7 

9 

11 

12 

10 

13. 

41 

40 

31 

41 

21 

41 

6 

8 

5 

9 

6 

7 

14. 

Divide  : 

8)32 

4)32 

9)36 

4)48 

7)28 

4)16 

15.  4  is  one  factor  of  16  tens,  what  is  the  other? 
Of  20  tens,  what  is  the  other?     How  often  is  6  con- 
tained in  24  tens  ?     8  in  32  tens?     4  in  8  hundreds? 

16.  Copy  and  divide  : 

4)164          4)208  6)246  8)328  4)804 

17.  8  +  1  =  ?  12  +  2  =  ?  24  +  ?  =  27 
4x2+1=?        4x   3+2=?        4x   6+?=27 

18.  What   number   smaller   than   9   has   4   for   a 
factor?  8-*-4  =  ?  9-5-4  =  ? 


100  ARITHMETIC 

19.  What   number   smaller   than   14   has   4   as   a 
factor?    Smaller  than  13?  15?  19?  21?  34?  35?  27? 

38? 

20.  Draw  on  the  board  lines  13  in.,  19  in.,  and 
31  in.  long.      Measure  each  line  with  a  4-in.  unit 
and  find  out  how  many  times  the  unit  measures  the 
lines  and  note  the  remainder  in  each  case. 

Divide  : 

21.  4  in.)13  in.  4  in.)19  in. 

4  yd.)34  yd.  4^)271 

22.  4)18       4)25       4)22       4)29       4)36       4)39 

Lesson  49 

1.  Take  any  two  points  less  than  a  yard  apart. 
Measure  the  distance  between  them  with  a  foot-rule 
and  also  with  a  yardstick  divided  into  inches. 

Write  your  results  thus  : 

1  ft.  8  in.  =20  in.  2  ft.  3  in.  =27  in. 

Practise  this  measuring. 

2.  1  ft.  6  in.  =  ?  in.  1  ft.  4  in.  =  ?  in. 
2ft.  4in.  =  ?in.                2ft.  6in.  =  ?in. 
3  ft.  3  in.  =  ?  in.                 4  ft.  2  in.=?  in. 

3.  How  can   you   change   2   ft.  4  in.  to   inches 
without  actually  measuring? 


LESSON   49  101 

4.  Take  any  two  points  less  than  a  yard  apart. 
Measure  the  distance   between  them  with  a  yard- 
stick and  also  with  a  foot-rule.     Express  your  results 
thus  : 

17  in.  =  1  ft.  5  in.  34  in.  =2  ft.  10  in. 

Practise  this  measuring. 

5.  15  in.  =?  ft.  ?  in.  18  in.  =?  ft.  ?  in. 
26  in.  =?  ft.  ?  in.              29  in.  =?  ft.  ?  in. 
39  in.  =?  ft.  ?  in.  0  in.  =  ?  ft.  ?  in. 

6.  How  can  you  change  26  in.  to  feet  and  inches 
without  actually  measuring? 

7.  Measure  a  gallon  of  water  with  a  quart  meas- 
ure.    What  number  do  you  get  ?     1  gal.  =  ?  qt. 

Measure  2  gal.    of  water  with  a  quart  measure. 
What  number  do  you  get  ?     2  gal.  =  ?  qt. 

8.  3  gal.  =  ?  qt.         5  gal.  =  ?  qt.         4  gal.  =  ?  qt. 
7  gal.  =  ?  qt.         6  gal.  =  ?  qt.         8  gal.  =  ?  qt. 

How  can  you  change  gallons  to  quarts  without 
actually  measuring  ? 

9.  Measure  8  qt.  of  water  into  a  pail.     Measure 
the  same  water  with  a  gallon  measure.     What  num- 
ber do  you  get?     8  qt.  =  ?  gal. 

10.   12  qt.  =  ?  gal.      20  qt.  =  ?  gal.      36  qt.  =  ?  gal. 
24  qt.  =  ?  gal.      16  qt.  =  ?  gal.      48  qt.  =  ?  gal. 

How  can  you  reduce  quarts  to  gallons  without 
actually  measuring? 


102  ARITHMETIC 

11.  Measure  1  gal.   3  qt.    of   water   into   a   pail. 
Measure  this  again  with  a  quart  measure.      What 
number  do  you  get  ?      1  gal.  3  qt.  =  ?  qt.      Measure 
in  a  similar  manner  other  quantities  of  water,  and 
write  your  results  as  before. 

12.  3  gal.  3  qt.  =?  qt.  5  gal.  2  qt.  =  ?  qt. 
7  gal.  2  qt.  =  ?  qt.  9  gal.  3  qt.  =  ?  qt. 
Ipt.     2gi.=?gi.  3pt.     2.gi.=?gi. 

How  do  you  reduce  3  gal.  2  qt.  to  quarts  ? 

13.  10  qt.  =  ?  gal.  ?  qt.  27  qt.  =?  gal.  ?  qt. 

9gi.=?pt.  ?gi.  18gi.=?pt.  ?gi. 

14.  1  hr.  =  ?  min.  2  hr.  30  min.  =  ?  min. 

3  hr.  10  min.  =  ?  min.      4  hr.  25  min.  =  ?  min. 

15.  2  wk.  4  da.  =?  da.  3  wk.  3  da.  =  ?  da. 

4  wk.  2  da.  =  ?  da.  26  da.  =  ?  wk.  ?  da. 

16.  4  yd.  3  ft.  =  ?  ft.  6  yd.  2  ft.  =  ?  ft. 
How  do  you  reduce  5  yd.  2  ft.  to  feet  ? 

16  ft.  =  ?  yd.  ?  ft.  23  ft.  =  ?  yd.  ?  ft. 

How  do  you  reduce  25  ft.  to  yards  and  feet  ? 

17.  A  road  is  6  yd.  2  ft.  wide.     What  is  the  width 
in  feet  ?     In  inches  ? 

18.  A  room  is  8  yd.  2  ft.  long.     How  many  steps 
will  a  boy  take  in  walking  the  length  of  the  room  if 
he  steps  2  ft.  each  time  ? 

19.  A  man  steps  30  in.  at  each  step.     How  many 
feet  and  inches  does  he  step  ? 


LESSON  50  103 

20.  How  many  times  will  a  pail  containing  2  gal. 
2  qt.  of  water  fill  a  quart  measure  ? 

21.  How  many  2-qt.  jars  will  hold  8  gal.  2  qt. 
of  fruit  ? 

22.  What  will  1  gal.  of  cream  cost  at  30^  a  qt.? 

23.  What  will  2  gal.  2  qt.  of  milk  cost  at  2^  a  pt.? 

24.  A  milkman  sold  1  qt.  of  milk  to  each  of  48 
customers.     How  many  gallons  did  he  sell  ? 

Lesson  50 

1.    Draw  an  oblong  4  in.  long  and  3  in.  wide. 
Divide  it  into  square  inches.     What  is  its  area  ? 


2.  If  each  dot  represents  1  sq.  in.,  how  many 
sq.  in.  are  represented  by  all  the  dots?    What  figure 
is  represented?     (An  oblong  4  in.  long  and  3  in. 
wide.) 

3.  If  each  dot  represents  1  sq.  ft.,  what  figure  is 
represented?     What  is  its  area?  1  sq.  yd.?  1  sq.  mi.? 

4.  Draw  an  oblong  6  in.  long  and  4  in.  wide. 
Represent  its  area  by  dots.      What   does  each  dot 
represent?     What  is  its  area? 

5.  What  is  the  area  of  an  oblong  6  ft.  long  and 
4  ft.  wide?    6  yd.  long  and  4  yd.  wide?    6  mi.  long 
and  4  mi.  wide  ? 


104  ARITHMETIC 

6.  Draw  an  oblong  5  yd.  long  and  4  yd.  wide, 
making  1  in.  stand  for  1  yd.     What   is   its   area? 
Could  the  same  drawing  represent  an  oblong  5  mi. 
long  and  4  mi.  wide?     What  would  1  in.  then  stand 
for  ?     What  area  would  it  then  represent  ? 

7.  What  is  the  area  of  each  of  these  oblongs? 

Length  Width  Length  Width 

5  in.  4  in.  8  yd.  4  yd. 

7  ft.  3  ft.  10  mi.  4  mi. 

9  ft.  3  ft.  12  mi.  3  mi. 

8.  Draw  an  oblong  3  in.  long  and  3  in.  wide. 
What  is  its  area? 

An  oblong  whose  length  is  equal  to  its  breadth 
is  a  square. 

9.  Draw  a  square  whose  side  is  4  in.     What  is  its 
area?     Could  the  same  drawing  represent  a  square 
whose   side  is  4  mi.?      What  area   would   it   then 
represent  ? 

10.  What  is  the  area  of  a  2-in.  square?    a  3-in. 
square  ?  a  4- in.  square  ? 

11.  How  many  square  inches  in  an  oblong  4  in. 
long  and  3  in.  wide? 

12.  Draw  an  oblong  4  2-in.  long  and  3  2-in.  wide 
and  divide  it  into  2-in.  squares.     How  many  ? 

13.  How  many  2-in.  squares  in  an  oblong  10  in. 
long  and  8  in.  wide  ?     Draw  the  oblong. 


LESSON   51  105 

14.  How  many  3-in.  squares  in  an  oblong  4  3-in. 
long  and  3  3-in.  wide  ?     Draw  the  oblong. 

15.  How  many  4-in.  squares  in  an  oblong  4  4-in. 
long  and  3  4-in.  wide  ?     Draw  the  oblong. 

16.  How  many  4-in.  squares  in  an  oblong  12  in. 
long  and  8  in.  wide  ? 

17.  If  6  is  one  factor  of  24,  what  is  the  other  ? 
An  oblong  is  6  in.  long  and  contains  24  sq.  in. 

How  wide  is  it?     What  is  its  perimeter  ? 

18.  An  oblong  is  5  mi.  long  and  contains  20  sq.  mi. 
What  is  its  perimeter  ?     How  many  hours  would  it 
take  a  person  to  walk  around  it  at  the  rate  of  3  mi. 
an  hour.     How  wide  is  it  ?     Draw  the  oblong. 

19.  What  is  the  side  of  a  square  which  contains 
4sq.  in.?  9  sq.  ft.?  16  sq.  yd.?  1  sq.  yd.?  16  sq.mi.? 

20.  A  blackboard  is  12  ft.  long  and  4  ft.  wide. 
How  many  square  feet  of  surface  has  the  board  ? 

21.  A  strip  of  carpet  is  9  ft.  long  and  3  ft.  wide. 
How  many  square  yards  does  it  contain  ? 

22.  A  strip  of  carpet  containing  24  sq.  ft.  is  2  ft. 
wide.     How  long  is  it  ?     How  many  yards  ? 

Lesson  51 

1.  At  4^  a  pt.,  what  will  5  qt.  of  raspberries 
cost? 

2.  At  6^  a  pt.,  how  many  quarts  of  raspberries 
will  cost 


106  ARITHMETIC 

3.  If  4  men  can  do  a  piece  of  work  in  7  da.,  how 
long  will  it  take  1  man  to  do  it  ?  2  men  ? 

4.  If  a  mail  earns  $4  a  day,  how  much  will  he 
earn  in  9  da.?     In  how  many  days  would  he  earn 
this  at  13  a  day? 

5.  If  a  man  earns  $3  a  day  and  spends  $2,  in 
how  many  days  will  he  save  $  36  ? 

6.  A  farmer  bought  4  cows  at  $30  a  head,  and  3 
sheep  at  $  6  each.     How  much  did  they  cost  him  ? 

7.  A  farmer  sold  30  sheep  at  $4  a  head  and  6 
lambs  at  $  3  each.     How  much  did  he  sell  them  for  ? 

8.  An  express  train  ran  5  hr.  at  the  rate  of  40 
mi.  an  hour.     How  far  did  it  go  ? 

9.  If  4  A.  of  land  cost  $320,  what  did  1  A.  cost  ? 

10.  A  dealer  bought  4  bicycles  at  $40  apiece  and 
sold  them  at  $  62  apiece.     What  was  his  gain  ? 

11.  Write  4  under  each  of. these  quantities  and 
multiply:  $32,  $61,  $72,  $208,  $322,  $421. 

12.  A  man  saves  $32  a  month.     How  much  will 
he  save  in  3  mo.? 

13.  What  is  the  value  of  24  yd.  of  cloth  at  $2  a 
y ard  ?     At  f  J  a  yard  ?     At  $  2£  a  yard  ? 

14.  If  a  man  pays  $4  a  week  for  board,  how  much 
does  he  pay  for  board  in  one  year  of  52  wk.? 

15.  If  4  doz.  eggs  cost  84^,  what  is  the  price  per 
dozen  ? 


LESSON  52  107 

Lesson  52 

1.  Divide   2£   4£  6£  8£  10  £  12  £  14  £   16  £ 

18  £20  £22  £24£  by  2. 

Take  l  of  2£  4£  6£  8£  10£  12£  14  £  16£  18£ 
20  <  22  £  24  £ 

How  do  you  find  one-half  of  a  quantity  ? 

2.  Divide   3£   6^,   9^,  12  £  15  £  18  £  21  £  24  £ 

27  £  30^,  33  £  36  £  by  3. 

Take  l  of   3£  6^,  9^,  12^,  15^,  18^,  2l£  24^, 
27^,  30^,  33^,  36^. 

How  do  you  find  one -third  of  a  quantity  ? 

3.  Divide  $8,  $20,  $12,  $32,  $4,  $16,  $36,  $28, 
$48,  $24,  $44,  $40,  by  4. 

Take  \  of  $20,  $32,  $40,  $36,  $48,  $24,  $8,  $16, 
$4,  $44,  $12,  $28. 

How  do  you  find  one-fourth  of  a  number? 

4.  If  a  yard  of  cloth  cost  24^,  what  will  ^  yd. 
cost?  \  yd.? 

5.  Divide  5  ft.,  10  ft.,  15  ft.,  20  ft.,  by  5.     Take 
^  of  5  ft.,  10  ft.,  15  ft.,  20  ft. 

How  do  you  find  one-fifth  of  a  quantity? 

6.  Divide  6  yd.,  18  yd.,  12  yd.,  24  yd.,  by  6. 
Take  £  of  6  yd.,  18  yd.,  12  yd.,  24  yd. 

How  do  you  find  one-sixth  of  a  quantity  ? 

7.  Divide   7  mi.,  14  mi.,   21  mi.,  28  mi.,  by  7. 
Take  \  of  7  mi.,  14  mi.,  21  mi.,  28  mi. 

How  do  you  find  one-seventh  of  a  quantity? 


108  ARITHMETIC 

8.  Divide  8  A.,  24  A.,  16  A.,  32  A.,  by  8.     Take 
|  of  8  A.,  24  A.,  16  A.,  32  A. 

How  do  you  find  one-eighth  of  a  quantity? 

9.  Divide  9,  18,  27,  36,  of  any  unit  by  9.     Take 

1  of  9,  18,  27,  36,  of  any  unit. 

How  do  you  find  one-ninth  of  a  quantity? 

10.  If  I  cut  a  piece  of  ribbon  36  in.   long  into 
fourths,  what  will  be  the  length  of  each  piece  ?     If 
into  sixths?     If  into  ninths? 

11.  Divide  20  lb.,  10  lb.,  40  lb.,  30  lb.,  by  10. 
Take  TV  of  20  lb.,  10  lb.,  40  lb.,  30  lb. 

How  do  you  find  one-tenth  of  a  quantity? 

12.  Divide  11  qt.,  33  qt.,  44  qt.,  22  qt.,  by  11. 
Take  -±.  Of  22  qt.,  11  qt.,  44  qt.,  33  qt. 

How  do  you  find  one-eleventh  of  a  quantity? 

13.  Divide  12  gal.,  24  gal.,  36  gal.,  48  gal.,  by  12. 
Take  ^  of  12  gal.,  24  gal.,  36  gal.,  48  gal. 

How  do  you  find  one-twelfth  of  a  quantity? 

14.  In  5  hr.  a  man  walked  20  mi.     How  far  did 
he  walk  in  1  hr.?     In  3  hr.? 

15.  If  6  times  Helen's  age  is  24  yr.,  how  many 
years  younger  is  she  than  her  sister  who  is  9  yr.  old  ? 

16.  How  much  will  6  bananas  cost  when  4  doz. 
cost  48^? 

17.  If   8  oranges  cost  32^,  what  is  the  price  of 

2  doz.  oranges  ? 


LESSON  53  109 

18.  Divide  36^  equally  among  12  children.    "What 
does  each  child  get? 

19.  If  1  yd.  of  ribbon  costs  40^,  what  will  ^  yd. 
cost  ?     If  2  yd.  cost  24^,  what  will  J  yd.  cost  ? 

20.  If  4  cows  cost  $ 120,  what  is  the  cost  of  each 
cow?     What  is  the  gain  on  selling  them  for  1 36 
apiece  ? 

21.  If  a  3-lb.  pail  of  lard  costs  24^,  what  is  the 
price  per  lb.?     What  is  saved  through  buying  a  5-lb. 
pail  for  39^? 

22.  If  12  bars  of  soap  cost  48 /,  what  will  1  bar 
cost  ?     What  will  6  bars  cost  ? 

23.  If  one  2-lb.  can  of  fruit  costs  22^,  what  will 
4  cans  cost? 

24.  If  2  5-lb.  boxes  of  biscuits  cost  64^,  what  will 
20  lb.  of  biscuits  cost? 

25.  Make  questions  using  the  following  table  of 
prices : 

Butter  22^  per  lb.  Olives  40**  per  pt. 

Corn     12  f  per  2-lb.  can.     Salt        7  f  per  10-lb.  sack. 

Fish        9^per£-lb.  can.     Soap       4^  per  bar. 

Lesson  53 


1.    In  this  arrangement  of  dots  what  can  each  dot 
represent  ? 


HO  ARITHMETIC 


?  |  of  12^  =  ?  f  of  12^=? 

|  of  12^=?  £of!2^  =  ?  fof!2^=? 

2.  Draw  a  line  12  in.  long  and  divide  it  into  4 
equal  parts. 

Jofl2in.  =  ?         |  of  12  in.  =?         fof!2in.  =  ? 
|  of  12  in.  =?         £of!2in.=?         fof!2in.  =  ? 

3.  How  do  you  find  J  of  a  quantity  ?  f  of  it  ?  f  ? 
£  ?     How  do  you  find  J  of  a  quantity  ?  -|  of  it  ? 

4.  A  boy  had  24  words  in  his  spelling  lesson  and 
spelled  correctly  -|  of  them.    How  many  did  he  spell 
correctly  ?     Represent  by  dots. 

5.  Make  6  dots   and   divide  them  into  3  equal 
groups.     Name  units  that  each  dot  can  represent. 

4  of  6  units  =  ?       *  of  6  units  =  ?        f  of  6  units  =  ? 

O  O  .0 

6.  Draw.  a  line  12  in.  long  and  divide  it  into  3 
equal  parts. 

£of!2in.  =  ?       fofl2in.  =  ?       Jo£15in.  =  ? 
fof!5in.  =  ?       lof!8in.=?       |ofl8in.=? 

7.  How  do  you  find  ^  of  a  quantity  ?  §  ? 

8.  Juliette  is  6  yr.  old  and  her  brother  Albert  | 
as  old.     How  old  is  Albert  ? 

9.  Jofl6  =  ?  |  of  16  =  ?  £of20  =  ? 
I  of  20  =  ?           £of24  =  ?  |  of  24  =  ? 

10.    Jft.  =  ?in.  |ft.=?in.  Jyd.  =  ?in. 

.  =  ?  in.         £  ft.  =  ?  in.          f  ft.  =  ?  in. 
?in.          |  yd.  =  ?  in.         |yd.=?in. 


LESSON  53  HI 

11.  J  hr.  =  ?  min.       |-  hr.  =  ?  min.      |  hr.  =?  min. 
Jda.=?hr.         fda.=?hr.         fda.=?hr. 
£da.=?hr.         fda.  =  ?hr.        £da.=?hr. 

12.  If  a  baby  sleeps  one-half  of  the  time,  how 
many  hours  a  day  does  he  sleep  ?     How  many  hours 
a  day  does  a  man  sleep  who  sleeps  one-third  of  the 
time  ? 

13.  |  of  15  =  ?  |  of  18  =  ?  f  of  24  =  ? 
f  of  21  =  ?           |  of  30  =  ?           |  of  36  =  ? 
|  of    6  =  ?           fof    9  =  ?  -I  of    5  =  ? 

o  o  o 

14.  If  I  cut  a  yard  of  ribbon  into  halves,  how 
many  pieces  will  I  have  ?     How  many  halves  in  a 
whole  ? 

15.  If  I  cut  a  yard  of  silk  into  thirds,  how  many 
pieces  will  I  have  ?     How  many  thirds  in  a  whole  ? 

16.  How  many  fourths  in  a  whole  ?    What  is  one- 
fourth  of  a  gallon  ?     How  many  quarts  in  a  gallon  ? 

17.  How  many  fifths  in  a  whole  ?     What  is  one- 
fifth  of  a  nickel  ?     How  many  cents  in  a  nickel  ? 
What  is  one-fifth  of  a  dime  ?     How  many  2-cents  in 
a  dime  ? 

18.  How   many   sixths   in    a   whole?     Sevenths? 
Eighths?    Ninths?    Tenths?    Elevenths?    Twelfths? 

19.  What  is  one-seventh  of  a  week  ?     How  many 
days  in  a  week?     What  is  one-tenth  of   a  dime? 
How  many  cents  in  a  dime?     What  is  one-twelfth 


112  ARITHMETIC 

of  a  foot?  How  many  inches  in  a  foot?  What  is 
one-twelfth  of  a  yard?  How  many  3-inches  in  a 
yard? 

20.  What  will  |  of  a  yard  of  cloth  cost  at  24  ^  a 
yard?     £  yd.?     f  yd.?     f  yd.?     £  yd.?     If  yd.? 

21.  fof8  =  ?     fof!6  =  ?    |  of  12  =  ?    How  do 
you  find  |  of  8?     Would  it  be  correct  to  multiply  8 
by  3  and  divide  by  4?    f  of  12  =  ?    f  of  32  =  ?    f  of 
24=?     |of8  =  ?     |  of  20=?     £of6  =  ? 

22.  l  da.  +1  da.  =  ?  hr.      1  da.  -  ^  da.  =  ?  hr. 
f  doz.  -  £  doz.  =  ?     |  doz.  -  |  doz.  =  ? 

23.  A  boy  bought  ^  doz.  oranges  and  ate  J  doz. 
How  many  were  left  ?     If  these  were  divided  equally 
among  3  boys,  how  many  did  each  boy  get  ? 

24.  If  1  ton  of  coal  lasts  30  da.,  how  long  will  J 
ton  last?     How  long  will  f  ton  last?     If  ^  ton  of 
coal  lasts  8  da.,  how  long  will  1  ton  last? 

25.  If  1  yd.  of  ribbon  is  worth  40^,  what  is  ^  yd. 
worth?     What  is  -|  yd.  worth?     If  ^  yd.  of  ribbon  is 
worth  6^,  what  is  1  yd.  worth  ? 

26.  A   melon  worth  40^  was   cut   into  4  equal 
pieces.     What  was  1  piece  worth  ?     3  pieces  ? 

27.  A  man  had  $24  and  spent  f  of  it  for  a  watch. 
What  did  the  watch  cost  him? 

28.  Monday,  James  rode  36  miles  on  his  bicycle, 
and  Tuesday  he  rode  -|  as  far.     How  far  did  he  ride 
on  Tuesday  ? 


LESSON  54 


Lesson  54 

1.  $8  is  the  quantity,  $2  the  unit,  what  is  the 
number?     4  is  often  called  the  ratio  of  $  8  to  $2. 

2.  How   often   is   the   unit   8   Ib.    contained   in 
32  Ib.  ?     What  is  the  ratio  of  32  Ib.  to  8  Ib.? 

3.  What  will  32  Ib.  of  flour  cost,  if  8  Ib.  cost 
22^? 

4.  4  gal.  is  one  of  the  3  equal  parts  of  12  gal. 
We  say  the  ratio  of  4  gal.  to  12  gal.  is  J.     What  is 
the  ratio  of  5  gal.  to  10  gal.  ?     Of  6  doz.  to  18  doz.  ? 

5.  What  is  the  ratio  of  4  A.  to  16  A.?     Of  the 
cost  of  4  A.  to  that  of  16  A.?     If  16  A.  cost  $800, 
what  will  4  A.  cost  ? 

6.  What  is  the  ratio  of  9^  to  27^?     9  dimes  to 
27  dimes?    9  25-ct.  pieces  to  27  25-ct.  pieces?     9  50- 
ct.  pieces  to  27  50-ct.  pieces  ?     9  of  any  unit  to  27  of 
the  same  unit  ? 

7.  What  is  the  ratio  of  the  price  of  6  bu.  of 
wheat  to  that  of  24  bu.?     If  24  bu.  of  wheat  cost 
120,  what  will  6  bu.  cost? 

8.  The  ratio  of  the  value  of  a  purse  to  the  money 
in  it  is  ^.     If  there  is  $  8  in  the  purse,  what  is  the 
value  of  the  purse  ? 

9.  Name  as  many  quantities  as  you  can  of  which 

2  is  the  ratio.     Of  which  1  is  the  ratio. 

10.    Name  as  many  quantities  as  you  can  of  which 

3  is  the  ratio  ;  ^  the  ratio  ;  4  the  ratio  ;  J  the  ratio. 

x 


114  ARITHMETIC 

11.  What  is  the  ratio  of  3  bu.  to  12  bu.?     24  Ib. 
to  8  Ib.?     1  pt.  to  1  qt.?     3  pt.  to  3  qt.?     1  qt.  to 
1  gal.?     3  qt.  to  3  gal.?     6  to  18  ?     12  to  3  ? 

12.  If  12  bu.  of  potatoes  cost  1 8,  what  will  3  bu. 
cost? 

13.  If  8  boxes  of  candy  weigh  4  Ib.,  what  will  24 
boxes  of  candy  weigh  ? 

14.  What  is  the  cost  of  18  bunches  of  firecrackers 
when  6  bunches  cost  30^? 

15.  If  3  boxes  of  berries  cost  30^,  what  will  18 
boxes  cost  ? 

16.  What  is  the  ratio  of  1  gal.  to  1  qt.  ?    Of  1  qt. 
to  1  gal.  ?     Of  4  qt.  to  4  gal.  ?     Of  3  gal.  to  3  qt.  ? 

17.  If  1  gal.  of  maple  syrup  is  worth  80^,  what  is 
the  value  of  1  qt.  ? 

18.  When  butter  is  worth  24^  a  Ib.,  how  much 
can  I  buy  for  12^? 

19.  If  cheese  is  worth  16^  a  Ib.,  how  much  can  I 
buy  for  4^ ?     How  much  for  12^? 

20.  When  eggs  are  12^  a  dozen,  how  many  can  I 
buy  for  36^?      For  6^? 

21.  If  1  qt.  of  milk  is  worth  6  ^,  what  must  I  pay 
for  1  gal.  2  qt.  1  pt.  ?     If  3  qt.  of  kerosene  are  worth 
10  ^,  what  are  3  gal.  worth  ? 

22.  John  has  2  dimes  and  James  7  times  as  much. 
How  much  have  they  together  ?     James  has   how 
much  more  than  John  ? 


LESSON  55  115 

Lesson  55 

1.  I  sold  a  cow  for  4  ten-dollar  bills  ;  how  much 
did  I  get  for  the  cow  ?     If  I  had  been  paid  in  live- 
dollar  bills,  how  many  would  I  have  got  ? 

2.  I  paid  3  five-dollar  bills  and  a  two-dollar  bill 
for  an  overcoat.    What  did  it  cost  me? 

3.  I  paid  12  two-dollar  bills  and  2  one-dollar  bills 
for  a  suit  of  clothes.     What  did  it  cost  me  ? 

4.  I  paid  in  dimes  30^  for  a  book.     How  many 
dimes  did  I  pay  ? 

5.  I   paid   in   nickels   20^   for   a    handkerchief. 
How  many  nickels  did  I  pay  ?     If   I  had  paid  in 
dimes,  how  many  ? 

6.  The  1  cent  piece,  the  5  cent  piece  (nickel),  the 
ten  cent  piece  (dime),  the  quarter  dollar  (25^),  the 
half  dollar  (50f),  and  the  dollar  (100^)  are  called 
coins  of  the  United  States. 

7.  I  bought  a  yard  of  ribbon  for  15^,  giving  3 
coins  in  payment.     What  was  the  value  of  the  coin  ? 

8.  I  bought  a  yard  of  cloth  for  60^,  giving  6  coins 
in  payment.     What  was  the  value  of  the  coin  ? 

9.  I  paid  50^  for  a  bushel  of  potatoes,  giving  2 
coins  in  payment.     What  was  the  value  of  the  coin  ? 

10.  I  bought  a  loaf  of  bread  for  6^,  giving  two 
coins  in  payment.     What  were  the  coins  ? 

11.  I  paid  15^  for  a  dozen  bananas,  giving  two 
coins  in  payment.     What  were  the  coins  ? 


116  ARITHMETIC 

12.  If   I   buy  a  pound   of  butter  for  25^,  with 
what  coins  can  I  pay  for  it  ? 

13.  I  bought  a  pound  of  meat  for  16^.     What 
three  coins  would  pay  for  it  ? 

14.  I  bought  a  dozen  eggs  for  22^.     What  coins 
would  pay  for  the  eggs  ? 

15.  These  coins  are  called  units  of  measure  because 
they  measure  the  value  of  things. 

16.  Name  all  the  units  of  measure  you  can,  that 
measure  the  value  of  things. 

17.  If  I  paid  4  five-dollar  bills,  a  two-dollar  bill, 
and  a  one-dollar  bill  for  an  overcoat,  how  much  did 
I  pay  in  all  ? 

18.  Jf  I  paid  3  ten-dollar  bills  and  a  five-dollar 
bill  for  a  suit  of  clothes,  and  received  in  change  a 
two-dollar  bill,  how  much  did  the  suit  cost  me  ? 

Lesson  56 


1.  |  doz.  —  %  doz.  =  ?     Your  answer  is  what  part 
of   a   doz.  ?     4   doz.  +  4-   doz.  =  ?     Your  answer  is 

o  o 

what  part  of   a  dozen  ?     -|  doz.  —  |  doz.  =  ?     Your 
answer  is  what  part  of  a  dozen  ? 

2.  1   ft. -^   ft.=  ?    in.       |    ft.  -1   ft.  =  ?   in. 
|  ft.  —  ^  ft.  =   ?  in.     Your  answer  is  in  each  case 
what  part  of  a  foot  ? 


LESSON  56  117 

3.  1  day  —  J  day  =  ?  hr.     J  day  —  J  day  =  ?  hr. 
|  day  +  ^  day  =  ?  hr.     Your  answer  is  in  each  case 
what  part  of  a  day  ? 

4.  1  hr.  +  £  hr.  =    ?   min.     J   hr.  -  J   hr.  =    ? 
min.      J    hr.  —  ^   hr.  =    ?    min.       Your   last    two 
answers  are  in  each  case  what  part  of  an  hour? 

5.  J  Ib.  +  $•  Ib.  =   ?  oz.     \  Ib.  +  |  Ib.  =   ?  oz. 
|  Ib.  —  ^  Ib.  =  ?  oz.     Your  last  answer  is  what  part 
of  a  pound? 

6.  f  gal.  -  1  gal.  =   ?  qt.     f  gal.  - 1  gal.  =   ? 
qt.      J  gal.  +  f  gal.  =   ?  qt.      Your  first  two  an- 
swers are  in  each  case  what  part  of  a  gallon  ? 

7.  From  a  pail  containing  |  doz.  eggs,  ^  doz.  are 
taken.     How  many  are  left  in  the  pail  ?     What  part 
of  a  dozen  ? 

8.  From  a  pitcher  containing  |  gal.  of  milk,  J 
gal.  is  poured.       How  many  quarts  are  left  in  the 
pitcher?     What  part  of  a  gallon? 

9.  What  is  the  cost  of  |  gal.  of  milk  at  6  ^  a  qt.  ? 

10.  Draw  a  line  1  ft.  long  and  divide  it  into  four 
equal  parts. 

What  part  of  a  foot  is  each  of  these  parts  ?     J  ft. 
=,*ft. 

11.  l   ft.  +  i   ft.  =  ¥   ft.      l   ft.  -  £  ft.  =    ?   ft. 
£ft. +f  ft.  =*=  ?ft. 

12.  lyd.  =¥yd.     lyd. +lyd.  =  ?yd.     \  yd.  + 
|  yd.  =  ?  yd.     f  yd.  +  \  yd.  =  ?  yd. 


118 


ARITHMETIC 


13.    Add: 

$21 


How  do  you  add  these  quantities  ? 
14.    Add  : 

8  20  6  4 


15.    Subtract  : 
8}  T} 


9} 


5} 


41 


10} 


How  do  you  subtract  these  numbers  ? 

16.    Copy  and  add  : 

12J     82J     531     25£ 
23J     16      14      14 


33} 


Lesson  57 

1.  Edward  is  31  yr.  old  and  John  4£.     What  is 
the  sum  of  their  ages  ? 

2.  James  has  1  21  and  Harry  $  5^.     How  much 
have  they  together  ? 

3.  John  has  |6f  and  Albert  $21.     How  much 
more  has  John  than  Albert  ? 

4.  A  table  is  4  ft.  long  and  21  ft.  wide.     What 
is  the  difference  between  its  length  and  width  ? 


LESSON  57  119 

5.  A  farmer  planted  f  of  a  field  with  corn  and 
the  rest  with  potatoes.     What  part  of  the  field  did 
he  plant  with  potatoes  ?     If  there  were  2  A.  of  pota- 
toes, how  many  acres  were  planted  with  corn  ? 

6.  What  is  .the  sum  of  f  and  £?     Of  {  and  f  ? 
Of  l  and  £?     Of  £  and  f>     Of  |  and  J?     Of  J 
andl? 

7.  What  is  the  difference  between  1  and  f  ?     1 
andj?     landj?     £  and  J?     fandj?     J  and  J? 

8.  Draw  a  line  1  ft.    long,  and  divide  it  into 
fourths.     How  many  fourths  in  1  ft.  ?     How  many 
fourths  in  1 J  ft.  ?     1  ft.  =  ^  ft.     1£  ft.  =  ¥  ft. 

9.  Draw  a  line  3  ft.  long  and  measure  it  with  a 
unit  one-fourth  of  a  foot  long.     What  number  do 
you  get  ?    3  ft.  =  ?  fourths  of  a  foot  ?    3  ft.  =  ¥  ft. 

10.  How  many  fourths  of  a  foot  are  there  in  2  ft.  ? 
3  f t.  ?     4  ft.  ?     5  ft.  ?     6  ft.  ?     How  do  you  reduce 
a  number  of  feet  to  fourths  of  a  foot  ? 

11.  Draw  a  line  4^  ft.  long,  and  measure  it  with  a 
unit  one-fourth  of  a  foot  long.     What  number  of 
units  do  you  get  ?     4J  ft.  =  ?  fourths  of  a  foot  ? 

12.  2£  ft.  =¥  ft.     3£  ft.  =¥  ft.     3f  ft.  =¥  ft. 
l±  f  t.  =  ¥  ft.     6f  ft.  =  T  ft.     8f  ft.  =  ¥  ft. 

How  do  you  reduce  5^  ft.  to  fourths  of  a  foot? 

13.  f  ft.  =  ?  ft.     |  ft.  =   ?  ft.     *£  ft.  =   ?  ft. 
f  ft.  =  ?  ft.  ?  in.      \5-  ft.  =  ?  ft.  ?  in. 


120  ARITHMETIC 

14.  1  gal.  =  ?  qt.      £  gal.  =  ?  qt.      f  gal.  =  ?  qt. 
7-1  gal.  =  ?  qt.     lOf  gal.  =  ?  qt.     12J  gal.  =  ?  qt. 

15.  What  is  the  cost  of  2^  gal.  of  milk  at  20^  a 

gal.? 

16.  8  qt.  ==  ?  gal.     12  qt.  =  ?  gal."    5  qt.  =  ?  gal. 
17  qt.  =  ?  gal.     34  qt.  =  ?  gal.     27  qt.  =  ?  gal. 

How  do  you  reduce  quarts  to  gallons  ? 

17.  f  qt.  =  ?  qt.    ?  pt.  -y-  qt.  =  ?  qt.    ?  pt. 
\5-  gal.  =  ?  gal.    ?  qt.      -^  Sal-  =  ?  Sal-    ?  ^k 

18.  Multiply: 

52f        71J        81f 


19.  What  is  the  cost  of  2  rugs  at  $22£  apiece  ? 

20.  Divide  : 

2)261       2)65       2)43       4)81       4)47       4)89 

21.  If  4  boys  divide  1 21,  which  they  earn,  equally 
among  them,  what  does  each  get  ? 

22.  Julian  rides  4  mi.  in  half-an-hour.    At  this  rate 
how  far  will  he  ride  in  2^-  hr.? 

23.  A  lady  paid  12^  a  yard  for  ribbon.     If  she  had 
paid  16^  a  yard,  it  would  have  cost  her  20^  more. 
How  many  yards  did  she  buy? 


SECTION  V 

Lesson  58 

1.  Cut  out  of  cardboard  units  1  in.,  2  in.,  3  in.,  •••, 
11  in.  long. 

2.  Select  five  pairs  of  units  which  put  end  to  end 
are  as  long  as  the  11-in.  unit. 

3.  With  these  five  pairs  of  units  and  the  11-in. 
unit  make  two   triangles,    each   of   whose   sides   is 
11  in.  long. 

4.  As  in  question  three,  make  a  square;    a  five- 
sided  figure ;  a  six-sided  figure,  each  of  whose  sides 
is  11  in.  long. 

5.  Memorize  the  sum  of  : 

2345  9876 

9876  2345 

6.  The  1  to  the  right  in  11  in.  means  one  unit  of 

1  in.     The  1  to  the  left  means  1  unit  of  10  in. 
What  does  the  1  mean  in  12  in.?     What  does  the 

2  mean?  • 

7.  Select  as  often  as  you  can  three  units  which 
placed  end  to  end  are  as  long  as  the  11-in.   unit. 
Write  your  results  in  columns  for  addition. 

121 


122  ARITHMETIC 


w        w        w        w 

8.  Draw  lines  through  the  above  arrangement  of 
dots  to  show  that  the  sums  found  in  question  5  are 
correct. 


9.  Draw  lines  through  the  above  arrangement  of 
dots  to  show  that  11  is  the  sum  of  each  of  the  follow- 
ing columns  for  addition. 

3246222724 
5443513073 
3532486424 

10.  A  grocer  buys  pineapples  at  8^  apiece,  and 
retails  them  for  11  ^  each.  How  much  does  he  gain 
on  every  dozen  he  sells  ? 


12.  Find  the  cost  of : 

-|  doz.  peaches  at  9^  a  doz. 
^  doz.  apples  at  6^  a  doz. 
£doz.  figs  at  8^  alb. 

13.  Add:   222334455 

919298287372666 

14.  Add;  *3        4423154 

32326224 
2515343742485463 

*  Add  thus  :  25,  28,  31. 


LESSON  59  123 

15.    Write  these  questions  under  each  other  and 
add:    |12,|4,$3;    $26,  $3,  $2;    3^,44^,3^;    5£ 


16.  I  paid  23^  for  a  book,  5^  for  a  block  of  paper, 
and  3^  for  a  lead  pencil.      How  much  did  I  pay 
in  all? 

17.  If  in  question  14  I  gave  the  clerk  3  dimes  and 
a  nickel,  what  change  did  I  get  back? 

Lesson  59 


1.  2  dimes  =  ?       4  dimes  =  ?X     6  dimes=  ? 

2  dimes  4^=  ?  f  5  dimes  6^  =  ?  t 
8  dimes  9^=  ?  f  7  dimes  20  =  ?  ^ 

2.  14^  =  1  dime  4£          64^=?  dimes  and  cents. 
25^  =  ?  dimes  and  cents.         88^  =  ?  dimes  and  cents. 
.32^  =  ?  dimes  and  cents.         90^  =  ?  dimes  and  cents. 

3.  25  Ib.  is  equal  to  2  10-lb.  (read  2  ten  Ib.)  and 
5  Ib.     Read  in  the  same  way  each  of  the  following: 
28  Ib.,  34  mi.,  23  sq.  mi.,  16  A.,  52  sq.  mi.,  2T  yr., 
49  da.,  15  hr.,  32  min.,  65  gal.,  65  qt.,  40  bu. 

4.  23  units  are  equal  to  2  tens  arid  3  units.     State 
how  many  tens  and  units  are  in  each  of  the  following 
number  of  units:  18,  50,  44,  72,  97,  9,  36. 

5.  2  tens  =  ?     4  tens  =  ?     8  tens  =  ? 

3  tens  5  units  =  ?  7  tens  4  units  =  ? 
2  tens  8  units  =  ?           6  tens  0  units  =  ? 
6  tens  6  units  =  ?  9  tens  5  units  =  ? 


124  ARITHMETIC 

6.  64  =  6  tens  4  units.  91  =  ?  tens  and  units. 
24  =  ?  tens  and  units.  40  =  ?  tens  and  units. 
82  =  ?  tens  and  units.  19  =  ?  tens  and  units. 
57  =  ?  tens  and  units.  77  =  ?  tens  and  units. 

7.  64  in.  =6  units  of  ten  inches  and  4  units  of  one 
inch. 

24  in.  =  ?        82  ft.  =  ?     57  yd.  =  ?    91  da.  =  ? 
15  hr.  =  ?     44  min.  =  ?     18  sec.  =  ?     85  Ib.  =  ? 

8.  Read:  11.25,  $2.50, 16.42,  87.08,  $4.44,  $9.25. 

9.  $256  is  equal  to  2  units  of  one  hundred  dol- 
lars, 5  units  of  ten  dollars,  and  6  units  of  one  dollar. 

256  yd.  is  equal  to  2  units  of  one  hundred  yards, 
5  units  of  ten  yards,  and  6  units  of  one  yard. 

10.  Read  as  in  question  9  each  of  the  following  : 
$625,  342  mi.,  705  A.,  432  sq.  mi.,  250  yd.,  999  yr., 
1099  yr.,  365  da.,  894  hr. 

11.  736  =  7  hundreds,  3  tens,  and  6  units. 
325  =  ?  hundreds,  tens,  and  units. 

415,  608,  840,  927,  1027,  265,  1265,  are  each  equal 
to  how  many  hundreds,  tens,  and  units  f 

12.  How  many  units  in  ten  ?      In  20  units  how 
many  tens?      In  40  units?      In  60  units?      In  80 
units  ? 

13.  In  18  units  how  many  tens  and  units?      In 
37  units  how  many  tens  and  units  ?     In  65  units  ? 
In  88  units?     In  96  units? 


LESSON  60  125 

14.  How  many  tens  in  one  hundred  ?     In  10  tens 
how  many  hundreds  ?     In  20  tens  ?     In  40  tens  ? 
In  60  tens?     In  80  tens? 

15.  In  18   tens   how  many  hundreds  and   tens? 
In  25  tens  how  many  hundreds  and  tens?     In  48 
tens?     In  67  tens?     In  84  tens? 

16.  4  hundreds  5  tens  2  units  =  ?  number. 

6  hundreds  4  tens  0  units  =  ?  number. 

7  hundreds  0  tens  8  units  =  ?  number. 
5  hundreds  3  tens  9  units  =  ?  number. 

8  hundreds  8  tens  8  units  =  ?  number. 

17.  Count  by  10's  from  0  to  100;   from  100  to 
200;  from  200  to  300. 

18.  Count  by  100's  from  0  to  1000;  from  1000 
to  2000;  from  2000  to  3000. 

Lesson  60 

%f        Add  thus:    8^  and  3^  are  11^,  or  1 

1.  28_^     dime  and  1^.     Write  down  1  and  add 

31^     the  1  dime  to  the  2  dimes,  making   3 

dimes.     Write  down  3.     The  sum  is 


2.    Add  as  in  question  1  : 

3^         5^         6^        2^         8         8         2  6 

48^       66^       54^       49^       83       42       99       105 


In  all  these  questions  you  carry  1  to  the  tens' 
column.     1  what  ? 


126 

AEITHMETIC 

Add: 

3. 

43 

38 

25   64 

35   27 

62 
58 

44 

77 

56   89 
45   30 

73 

39 

4. 
5. 

223 
474 

234 

635 

226 

342 

308 
443 

420 

427 
384 

279 
641 

396 

825 

314 

314 

392 

523 

203 

135 

182 

204 

225 

212 

174 

316 

421 

215 

642 

6.    Add,  placing  the  sum  above  the  line  : 

68 


23 

33 

13 

62 

25 

16 

32 

35 

45 

62 

28 

28 

46 

34 

19 

66 

Subtract  : 

7. 

68 

95 

*41 

60 

71   90 

81 

51 

45 

62 

28 

28 

35   42 

33 

16 

999 

816 

808 

741 

601 

1051 

• 

367 

254 

728 

503 

257 

342 

9.  A  man  paid  $165  for  a  horse  and  $225  for  a 
carriage  ?     How  much  did  he  pay  for  both  ? 

10.  An  arithmetic  costs  45^,  a  reader  36^,  and  a 
grammar  30  $.     How  much  did  they  all  cost  ? 

*  Subtract  thus  :  8  and  3  are  11  ;  carry  1  to  2  as  in  addition, 
making  it  3  ;  3  and  1  are  4.  Write  3  under  8  and  1  under  41 
2  thus,  28 

That  is,  fancy  you  are  doing  addition  with  the  sum  at  the  top.      13 


LESSON  61  127 

11.  A  man  bought  a  lot  for  $  975  and  sold  it  for 
1 850.     How  much  did  he  lose? 

12.  I  paid  11.25  for  a  roast  of  beef  and  11.10  for 
potatoes.     What  did  I  pay  for  both? 

13.  A  farmer  sold  his  wheat  for  $854  and  hay  for 
1237.     How  much  did  he  get  for  both? 

14.  A  merchant  took  in  1 332  on  Monday,  $204 
on  Tuesday,  and  $455  on  Wednesday.     How  much 
did  he  take  in  on  these  three  days  ? 


Lesson  61 

i. 

Memorize  the  sum  of  : 

3 

4 

5 

6 

9 

8 

7 

6 

2. 

Find  the  sum  of  : 

9 

8 

7 

6 

3 

4 

5 

6 

Add: 

3.  39565473 
19       13       26        36        77       48       65       38 

4.  44553323 
44263933 

22        34        44        51        63        70       85       96 

5.  What  is  the  cost  of  : 

4  Ib.  raisins  at  8^  a  Ib.? 
lib.  dates  at  6^  a  Ib.? 
Jib.  nuts  at  12^  a  Ib.? 


128  ARITHMETIC 


6.  *5 

*2 

3 

4 

1 

4 

2 

4 

4 

5 

3 

8 

3 

4 

2 

4 

2 

1 

3 

4 

5 

5 

5 

4 

14 

56 

33 

70 

65 

43 

26 

84 

7.  18 

26 

33 

53 

34 

28 

57 

23 

42 

36 

62 

74 

48 

92 

65 

88 

8.  748 

121 

643 

232 

495 

355 

161 

234 

879 

586 

497 

307 

565 

768 

In  each 

of  these  questions  you 

carry 

1.  This  1 

is  1  what? 

9.  426 

284 

294 

325 

272 

444 

111 

343 

303 

125 

254 

416 

333 

444 

212 

241 

702 

411 

412 

222 

555 

10.    What  is  the  cost  of : 

J  bu.  apples  at  60^  a  bu.? 
21  Ib.  biscuits  at  8^  a  Ib.? 
4  Ib.  sugar  at  5-J^  a  Ib.? 
Subtract : 

989     t521       625       930       641       989       862 
752       263       283       615       228       457       129 


11. 


*  Add  thus :  14,  16,  20,  25  ;  56,  57,  62,  64. 

t  Subtract  thus  :  3  and  8  are  11  ;  carry  1  to  6,  as  in  addition, 
making  it  7  ;  7  and  5  are  12  ;  carry  1  to  2  making  it  3 ;  3  and  2 
are  5.  That  is,  fancy  you  are  doing  addition  with  the  sum  at 
the  top. 


12. 


13. 


LESSON  62  129 

4564      7498      7594       8989  9387  7845 

2342      4288       6571       6363  8326  6043 

7982      9322      5745       4102  7629  1521 

2646       4218       2730       2052  1038  1432 


14.  A  farmer  has  638  sheep  in  one  flock  and  234 
in  another.     How  many  has  he  all  together  ? 

15.  I  bought  a  house -for  $4825  and  sold  it   for 
$  3460.     How  much  did  I  lose  ? 

16.  A  man  spent  $124  on  Monday,  $423  on  Tues- 
day, and  $673  on  Wednesday.     How  much  did  he 
spend  all  together  ? 

17.  How  many  days  are  there  in  April,  May,  and 
June  ?     How  many  days  are  there  in  July,  August, 
and  September  ? 


Lesson  62 

4 
987456 


l.    Memorize  the  sum  of  : 


Add: 

2.  58495538 
18       15       39       34       47       68       78       85 

3.  46359644 
54534343 

31       23       44       65       60       72       82       96 


130  ARITHMETIC 


4. 

1 

3 

4 

2 

4 

8 

2 

4 

3 

2 

2 

3 

2 

1 

3 

4 

3 

4 

2 

5 

1 

6 

3 

4 

12 

21 

34 

41 

56 

63 

73 

71 

5.  What  is  the  cost  of : 

4  yd.  of  elastic  at  6^  a  yd.? 
10yd.  of  tape  at  2^  a  yd.? 
2J  yd.  lining  at  10^  a  yd.? 
J  yd.  ribbon  at  4^  a  yd.? 

6.  28        38        27        39       25       33       56       40 
33       45        54        63       78       99       82       98 

7.  235     248      427      655     568     909      263     566 
548     671      496     714     815     204     574     546 


8.  Find  the  cost  of  2  bu.  of  potatoes  at  40^  &  bu., 
and  3J  Ib.  of  meat  at  12  X  a  Ib. 

9.  212     141      504     141      333     333      634     232 
154     320      412     453     444      111      307     260 
702     168      183     138     555     666      241     318 


Subtract : 

10.  674  954  439  715  609  938  310  609 
231823275438546444154352 

11.  6739  4903  6048  7354  3429  6336  7273  5128 


2435  2701  2035  1321  2316  2332  3123  4128 


LESSON  63  181 

12.    8653   9125   3522   4175   4967   2364    6001    5385 


7439  4135   2140   3514   3643   1423    3453    2962 

13.  A  farmer  received  $  235  for  his  corn  and  $ 470 
for  his  wheat.     How  much  did  he  receive  for  both  ? 

14.  A  cattle  dealer  had  3245  cattle  and  sold  1340. 
How  many  had  he  left  ? 

15.  A  man  bought  a  farm  for  $8225  and  sold  it 
for  $ 9415.     How  much  did  he  gain  ? 

16.  If  a  man  earns  12500  a  year,  and  his  expenses 
are  $1500,  how  much  does  he  save? 

17.  Find  the  sum  of  121, 121,  121,  121.     Multiply 
121  by  4. 

18.  Mr.  Brown  owed  Mr.  Smith  $225.     He  paid 
the  debt  by  giving  him  $160  and  a  horse.     What 
was  the  horse  worth? 


Lesson  63 

1.  Count  by  5's  from  5  to  200. 

2.  Memorize  : 

Five  times 


lis    5 

5  is  25 

9  is  45 

2  is  10 

6  is  30 

10  is  50 

3  is  15 

7  is  35 

11  is  55 

4  is  20 

8  is  40 

12  is  60 

132  ARITHMETIC 

3.  Give   two   i  actors   of    each    of   the   following 
numbers:  28,   45r  44,  32,  55,  27,  60,  48,  40,  35. 

4.  Give   the   two   equal   factors   of   each  of   the 
following  numbers  :    4,  9,  16,  25. 

5.  Give  as  many  pairs  of  factors  as  you  can  for 
each  of  the  following  numbers  : 

24<2  x  12,  3  x  8,  4  x  6),  12,  18,  20,  28,  30,  36,  40. 

6.  4  is  a  factor  of  12.     What  is  the  other  factor? 
4  is  a  factor  of  20.     What  is  the  other  factor  ? 

4  in  a  common  factor  of  12  and  20. 
Draw  lines  12  in.  and  20  in.  long  and  measure 
them  with  a  4-in.  unit.     How  many  units  in  each  ? 

7.  What  number  is  a  common  factor  of  20  and 
25  ?     Of  9  and  12  ?     Of  25  and  30  ?    Of  10  and  14  ? 
Of  12  and  15  ? 

8.  How  long  is  the  unit  that  will  exactly  measure 
two  pieces  of  ribbon  one  12  in.  long  and  the  other 
15  in.     With  what  coin  can  you  pay  a  debt  of 
and  also  of 


Multiply  : 

9.     21         *23  33  51  63  42 

555555 


*  Multiply  thus :  5  times  3  is  15 ;  write  down  5  and  carry  1 ; 
5  times  2  is  10 ;  10  and  1  are  11 ;  write  down  11.  The  product  is 
115. 


LESSON  63  133 

In  multiplying  23  by  5  you  carry  1.     This  1  is 
1  what  ? 


10. 

262 

341    424 

521    203 

313 

2 

3     4 

5     5 

5 

11. 

6 

5    5    4 

555 

5 

5 

687 

7    9   12 

10 

12. 

41 

52     42 

50     53 

52 

6 

6     7 

7      8 

9 

13.  James  rode  33  mi.  on  his  bicycle  in  one  week, 
and  Henry  4  times  as  far  all  but  12  mi.     How  far 
did  Henry  ride  ? 

14.  Divide : 

5)45      5)450      8)40      7)350      9)45      6)300 

15.  What  number  smaller  than  12  has  5  for  a 
factor?   smaller  than  16?   18?   22?   28?   33?   36? 
39?  42?  47?  49? 

Divide  : 

16.  *5)215    5)315    5)325    5)280    5)365    5)390 

On  dividing  325  by  5  you  have  a  remainder  2  on 
the  first  division.  This  2  is  2  what  ? 

*  Divide  thus  :  5  is  contained  in  21  4  times  with  remainder  1 ; 
write  down  4  ;  5  is  contained  in  15  3  times ;  write  down  3.  The 
quotient  is  43. 


134 


ARITHMETIC 


17.  4)212     3)252     5)375     4)304     2)572     3)291 

There  is  a  remainder  on  the  first  division  each 
time.     Is  this  remainder  units,  tens,  or  hundreds  ? 

18.  6)312     7)294     8)416     5)340     9)369     9)468 

19.  At  $  5  a  bbl.  how  many  barrels  of  flour  will 
cost  1325? 

20.  How  many  miles  an  hour  must  a  train  travel 
to  go  272  mi.  in  8  hr.  ?    In  6  hr.  ? 

21.  If  a  train  travels  26  mi.  an  hour,  how  far  dis- 
tant is  a  city  which  it  will  reach  in  4J  hr.  ? 

22.  A  farmer  received  $128  for  a  cow  and  some 
lambs.     He  received  $32  for  the  cow  and  $3  for 
each  lamb.     How  many  lambs  did  he  sell  ? 

Lesson  64 

1.  1x6=    6     6xl=?    4x6=24    6x4=? 
2x6=12     6x2=?     5x6  =  30     6x5=? 
3x6  =  18     6x3=?     6x6=?       6x6=? 

2.  Count  by  6's  from  6  to  72. 

3.  Memorize  : 

Six  times 


lis    6 

5  is  30 

9  is  54 

2  is  12 

6  is  36 

10  is  60 

3  is  18 

7  is  42 

11  is  66 

4  is  24 

8  is  48 

12  is  72 

LESSON   64  135 

4.  Give  two  factors  of  each  of  the  following  num- 
bers :  30,  21,  48,  54,  55,  72,  27,  66,  42,  60. 

5.  Give  as  many  pairs  of  factors  as  you  can  of 
each  of   the  following  numbers  :    18(2  x  9,  3  x  6), 
16,  36,  48,  24,  54,  60,  44. 

6.  What  number  is  a  common  factor  of  12  and 
15?     15  and  25?     22  and  33  ?     30  and  42?     28  and 
32? 

7.  Two  logs,  one  15  ft.  and  the  other  25  ft.  in 
length,  were  cut  into  the  longest  possible  pieces  of 
equal  length.     What  is  the  length  of  each  piece  ? 

Multiply  : 

8.  *49         24  35  47  58  66 

J5         _6  _6  _6  _6          _6 

In  multiplying  49  by  6  you  carry  5.     This  5  is 
5  what  ? 

9.  A  dealer  bought  84  sheep  at  $  6  apiece,  and 
sold  them  for  $600.     Find  his  gain. 

10.  396        396         396         396         396         506 
_2        _3          _j*          _5          _j6  6 

In  multiplying  396  by  3  you  carry  1.     This  1  is 
1  what  ?     You  also  carry  2.     This  2  is  2  what  ? 

11.  86566655 
68         9         7          9        12        12        11 

*  Multiply  thus  :  6  times  9  is  54  ;  write  down  4  and  carry  5  ;  6 
times  4  is  24 ;  24  and  5  are  29  j  write  down  29,    The  product  is  294, 


136  ARITHMETIC 

12.  22  34  83  75  36  66 

978698 

13.  A  farmer's  barn  cost  him  $225,  and  his  house 
9  times  as  much.     Find  the  cost  of  both. 

14.  Divide: 

6)426      8)400      6)546       9)549       5)505       9)369 

15.  What  number  smaller  than  20  has  6  for  a 
factor?     Smaller  than  15?     17?     26?     29?     34? 
38?    47?    49?     52?     58? 

Divide : 

16.*   6)150     6)324    6)456    6)294    6)402    6)732 

17.  2)576     3)576    4)576     5)650     6)864     6)834 

18.  4)704     6)702     5)735     7)448     8)448     9)459 

19.  6)594     9)594     8)520     7)364     8)504     9)504 

20.  Divide  the  contents  of  240  bags  of  oats  equally 
among  three  bins.     How  much  in  each  ? 

"  21.    How  many  bushels  of  wheat  in  24  bags  each 
containing  2  bu.,  and  18  bags  each  containing  3  bu.? 

22.  I  paid  i  240  for  a  horse  and  bicycle.  If  the 
horse  cost  5  times  as  much  as  the  bicycle,  find  the 
cost  of  each. 

*  Divide  thus :  6  is  contained  in  15  2  times  with  remainder  3  ; 
write  down  2  ;  6  is  contained  in  30  5  times ;  write  down  5.  The 
quotient  is  25. 


SECTION  VI 


Lesson  65 

l.  82.75  is  read,  two  dollars  and  seventy-five 
cents.  The  decimal  point  (.)  separates  dollars  from 
cents.  All  the  figures  to  the  left  of  the  decimal 
point  denote  dollars,  and  the  first  two  figures  to  the 
right  denote  cents. 


2.  Read  the  following  : 
$2.43       136.10       162.24 
$4.29       164.76       143.60 

3.  Read  the  following  : 


1169.65 
$691.80 


$1864.86 
$1759.45 


$.15,    $.05,    $.08 


4.  Read  the  following  : 

$.05              $   .07              $  15.17  $  204.04 

$.09               $   .30               $   77.60  $   300.06 

$.01              $   .75              $  20.05  $   300.60 

$.12               $2.16               $291.98  $1732.25 

$.18               $3.04               $201.64  $5300.20 

$.69               $5.20               $311.20  $6040.06 

5.  Write  in  figures  as  in  question  4  :  Three  dol- 
lars and  twenty-five  cents ;  thirty-seven  dollars  and 

137 


138  ARITHMETIC 

fifty  cents  ;  sixteen  cents  ;  eighty-three  cents  ;  four 
cents  ;  nine  cents  ;  twenty  dollars  and  six  cents. 

6.  Write  in  figures  :  One  hundred  nineteen  dol- 
lars and  twenty-five  cents  ;  two  hundred  forty -three 
dollars   and   ninety-one   cents ;    six   hundred   eight 
dollars  and  eight  cents ;   nine  hundred  ninety-nine 
dollars  and  ninety-nine  cents. 

7.  How  many  cents  in  $ 2 ?    In  $.25?    In  $2. 25? 

8.  How  many  cents  in  ?  — 

$3.75          $8.19         $4.06         $25.64          $10.06 
$6.07          $3.10         $6.43         $34.08         $20.20 

9.  Write  and  read  as  dollars  and  cents : 

16  £   6£   300  f,  210  £  625  £  409  £  2463  £   1250  £ 
2400  £  1650  £  1825  £ 

10.  How  many  cents  in  $£,  $  J,  $|,  $1,  $JL? 

11.  Write  as  dollars  and  cents  : 

$5J,     $6J,     $8f,     $12£,     $24f,     $43TL,     $64^. 

12.  How  many  dollars,  dimes,  and  cents  in  ?  — 
$2.45,          $6.40,          $3.08,          $4.00,          $.90. 

13.  How   many   ten-dollars,   dollars,   dimes,   and 
cents   in   $36.25,   $40.16,   $62.01,   $3.04,   $11.11? 
How  many  cents  in  1  dime?     Dimes  in  1  dollar? 
Dollars  in  1  ten-dollar  ? 

14.  Add: 

<£2.14  $13.21  $215.42  $1212.33 

3.20  22.16  211.00  2104.12 

4.53  24.00  420.06  3013.41 


LESSON   65  139 

15.  Find  the  sum  of  124.33,  121.14,  and  117.22. 
Find  the  sum  of  1134.25,  $243.40,  and  $510.53. 

16.  What  will  it  cost  to  settle  a  grocery  bill  of 
$22.33,  a  meat  bill  of  $14.12,  and  a  drug  bill  of 
$2.14? 

17.  Subtract : 

$8.75  $53.92  $369.43  $2146.56 

3.42  12.60  328.12  1013.45 

18.  What  is  the  difference  in  cost  between  two 
rocking-chairs,   one  costing  $27.75   and   the    other 
$16.50? 

19.  I  buy  a  chair  for  $2.65  ;  what  change  should 
I  get  back  from  a  five-dollar  bill  ? 

20.  Multiply  : 

$5.23               $22.15               $31.51               $213.42 
3  4  5  6 

21.  What  is  the  cost  of  5  T.  of  coal  at  $  6.25  a  ton, 
and  2  cords  of  wood  at  $4.25  a  cord  ? 

22.  Find  the  value  of:  $48.26-2;  $82.50-5-3; 
$.92-4;  $.06-2;  $628.75-j-5;  $483.90-=-6. 

23.  If  an  agent  makes  $  994.60  in  4  mo.,  what  are 
his  average  monthly  earnings  ? 

24.  Find  the  cost  of  : 

6  cups  at  $   .20  apiece. 

4  knives        at  $1.25  apiece. 

5  plates          at  $   .25  apiece. 

2  spoons        at  $1.50  apiece. 

3  salt  dishes  at  $   .25  apiece, 


140  ARITHMETIC 

Lesson  66 

1.  A  pitcher  holds  3  pt.     How  many  quarts  and 
pints  does  it  hold?     How  many  quarts  and  pints  in 
5  pt.  ?     9  pt.  ?     7  pt.  ?     11  pt.  ? 

2.  In  adding  pints,  what  unit  can  you  always  put 
in  place  of  every  2  pt.? 

3.  In  one  pail  there  are  2  qt.  1  pt.  of  water ;  in  a 
second  pail  3  qt.  1  pt.  ;  in  a  third  1  gal.  1  pt.     How 
much  water  in  the  three  pails  ? 

4.  Measure,  and  prove  your  answer  to  question 
3  correct. 

5.  Make  problems  like  question  3. 

6.  How  many  gallons  and  quarts  are  there  in 
6qt.?     9qt.  ?     5  qt.  ?     7  qt.? 

7.  What  unit  of  measure  can  you  put  instead  of 
every  4  qt.  in  a  quantity  of  liquid  ? 

8.  How  many  quarts  and  pints  in  3  cans,  each  of 
which  holds  5  pt.  ?     How  many  gallons,  quarts,  and 
pints  in  3  cans,  each  of  which  holds  7  pt.  ? 

9.  If  3  pieces  of  ribbon  of  the  same  length  cost 
$.15,  what  will  1  piece  cost? 

10.  Draw  a  line  three-quarters  of  a  yard  long, 
and  divide  it  into  pieces  each  one-quarter  of  a  yard 
long.  How  many  pieces?  What  is  the  cost  of  each 
piece  if  all  costs  18^?  Of  4  such  pieces?  How 
long  will  4  such  pieces  be  ? 


LESSON  66  141 

11.  If   three-quarters  of  a  yard  of  ribbon  costs 
what  will  one-quarter  of  a  yard  cost?     Four- 
quarters  of  a  yard  ?     One  yard  ?     One  yard  and  one- 
quarter  ? 

12.  If  |  yd.  of  cloth  costs  21 £  what  is  the  cost  of 
1  yd.  ?     How  do  you  find  the  cost  of  1  yd.  of  cloth 
when  you  know  the  cost  of  |  yd.  ? 

13.  If  ^  Ib.  of  butter  cost  24  ^,  what  is  the  price 
per  Ib.  ?     When  you  know  the  cost  of  |  Ib.  of  butter, 
how  do  you  find  the  cost  of  1  Ib.  ?     Of  1J  Ib.  ? 

14.  A  boy  sold  6  qt.  of  berries  at  6^  a  qt.     How 
many  oranges  at  3^  each  could  he  buy  with  the 
money  he  got  for  the  berries  ?     What  unit  measures 
the  value  of  an  orange  ? 

15.  When  milk  costs  24^  a  gallon,  what  is   the 
cost  of  1  qt.  ?     What  is  the  cost  of  1  pt.  ?     Of  1  gal. 
3  qt.  1  pt.  ?     What  is  the  cost  of  2  gal.  3  qt.  1  pt. 
at  2  f  a  pt.  ? 

16.  A  man  spent  f  of  his  salary.     What  part  of 
it  did  he  save  ?     If  he  had  spent  f  of  his  salary,  what 
part  would  he  have  saved?     If  this  was  $120,  what 
was  his  salary? 

17.  A  watch  cost  $50,  which  was  five  times  the 
value   of   the   chain.      What   was   the   cost   of   the 
chain?      Of  both?      What   is   the  whole  quantity 
here  ?     What  is  the  number  ?     What  is  the  unit  ? 


142  ARITHMETIC 

18.  Draw  a  square  whose  side  is  4  in.     Divide  it 
into  2-in.  squares.     How  many?     Name  the  whole 
quantity,  the  unit,  and  the  number.     How  did  you 
find  the  number  ? 

19.  How  many  2-in.   squares  in  a  square  whose 
side  is  6  in.  ?     8  in.?     10  in.  ?     1  ft.  ? 

20.  How  many  more  3-in.  squares  can  be  cut  from 
a  square  whose  side  is  12  in.  than  from  one  whose 
side  is  9  in.  ? 

21.  How  many  4-in.  squares  in  an  oblong  12  in. 
by  20  in.  ?     1  ft.  8  in.  by  3  ft.  ?     How  many  tiles, 
each  4  in.  square,  are  needed  for  a  piece  of  tiling 
4  ft.  long  and  1  ft.  4  in.  wide  ? 

Lesson  67 

1.  A  milkman  has  4  gal.  1  qt.  of  milk  in  one 
can  ;    in   another  3  gal.    1    qt.    1  pt.  ;    in  a  third 
2  qt.  1  pt.     How  much  milk  has  he  ? 

2.  A  milkman  sold  3  cans  of  milk,  each  contain- 
ing 2  gal.  3  qt.     How  much  did  he  sell  ? 

3.  How  many  quarts  in  5  gal.  2  qt.  ?     To  how 
many  customers  can  a  milkman  sell  5  gal.  2  qt.  if 
he  sells  2  qt.  to  each  customer?     Name  the  quan- 
tity, the  unit,  and  the  number. 

4.  If   I   divide   8  gal.   3   qt.   of  syrup   equally 
among  5  persons,  how  much  does  each  get?     In  this 


LESSON  143 

question  you  are  given  the  quantity  and  the  number 
and  are  required  to  find  the  unit.  State  the  ques- 
tion in  which  you  are  given  the  quantity  and  unit  to 
find  the  number. 

5.  A  man  buys  milk  at  4^  a  qt.,  and  sells  it  at 
3^  a  pt.     How  much  does  he  gain  on  each  gal.  ? 
How  much  on  6  gal.  ? 

6.  If  three-quarters  of  a  yard  of  cloth  cost  18  ^, 
what  will  one-quarter  of  a  yard  cost  ?     Four-quarters 
of  a  yard  ?     One  yard  ?     One  yard  and  one-half  ? 

7.  If  |  yd.  of  ribbon  costs  27  ^,  what  will  1  yd. 
cost?     1J  yd.?     If  -|  Ib.  of  raisins  cost  15^,  what 
will  1  Ib.  cost  ?     21  Ib.  ? 

8.  The  desks  in  a  schoolroom  cost  172  at  $2  a 
desk  ;  how  many  desks  are  there  in  the  room  ?     How 
many  rows  of  desks  with  6  in  a  row  ? 

9.  If  |  of  the  number  of  desks  in  a  room  are  33, 
how  many  desks  are  in  the  room  ?     How  do  you  find 
a  number  when  you  are  given  |  of  it? 

10.  A  milkman  sold  milk  at  $.03  a  pint.     What 
was  the  price  per  gallon  ?     What  will  5  gal.  sell  for  ? 

11.  James  paid  $-|  for  a  book  and  $ J  for  a  slate. 
How  much  more  did  the  book  cost  than  the  slate  ? 
How  much  did  both  cost  ? 

12.  A  milkman  having  25  gal.  2  qt.,  sold  -J  of  it. 
How  much  did  he  sell?     If  he  had  sold  |-  of  it,  how 
much  would  lie  have  sold  ? 


144  ARITHMETIC 

13.  A  farmer  sold  6  doz.  eggs  to  a  grocer  at  $.12 
a  doz.,  5  Ib.  of  butter  at  $.18  a  Ib.     He  took  his 
pay  in  sugar  at  6^  a  Ib.     How  many  pounds  of  sugar 
did  he  receive  ? 

14.  Florence  paid  $.64  for  an  arithmetic  and  ^  as 
much  for  a  reader.      What  did  both  cost  ?     What 
change  should  she  get  back  from  a  dollar  bill  ? 

15.  My  hens  lay  5  eggs  a  day.     In  how  many 
weeks  will  they  lay  140  eggs  ? 

16.  What  will  2  doz.  apples  cost  at  the  rate  of 
2  apples  for  3^  ?     What  is  the  unit  here  ? 

17.  How   many   feet   long   is   your   schoolroom? 
How  many  feet  wide  ?     Now  find,  without  measur- 
ing, the  number  of  yards  it  is  half-way  around  the 
room.     Test  your  answer  by  measuring. 

18.  A  boy  earns  $.09  an  hour,  and  works  8  hr.  a 
day.     How  much  more  does  he  earn  in  1  wk.  than  a 
boy  who  earns  $ .  10  an  hour,  and  works  7  hr.  a  day  ? 

19.  In  question  20,  place  one  dot  for  each  dollar 
left.       How  many  ?      How  many  dots  should  you 
place   for  the   money   spent   for   groceries  ?      How 
many  for  what  was  in  my  purse  at  first  ? 

20.  I  spent  f  of  the  money  in  my  purse  for  gro- 
ceries, and  had  $5  left.     What  part  of  my  money 
did  I  have  left  ?     How  much  had  I  at  first  ? 

21.  What  three  different  coins  make  $  .16  ? 


LESSON  68  145 

Lesson  68 

1.  Monday  a  boy  picked  5  qt.  1  pt.  of  berries, 
Tuesday  4  qt.  1  pt.,  and  Wednesday  6  qt.    1  pt. 
How  much  did  he  pick  on  these  three  days  ? 

2.  The  boy  in  question  1  sold  his  berries  at  6^  a 
quart,  and  bought  a  ball  and  bat  with  the  money. 
What  did  he  pay  for  the  ball  and  bat  ? 

3.  What  is  the  cost  of  6  qt.  1  pt.  of  milk  at  f  .24 
a  gallon  ? 

4.  What  will  3J  yd.  of  ribbon  cost  at  12^  a  yard  ? 
Of  the  three  terms,  quantity,  unit,  number,  which 
are  you  given  and  which  must  you  find  ?     Using  the 
same  numbers,  state  a  question  in  which  you  are 
given  the   quantity  and  unit  to  find  the  number. 
State  a  question  in  which  you  are  given  the  quantity 
and  number  to  find  the  unit. 

5.  School  is  in  session  from  nine  to  twelve  o'clock, 
and  from  a  quarter  after  one  to  half -past  three.     This 
is  how  many  hours  a  day?      Count  on  the  clock. 
How  many  hours  a  week  ? 

6.  If  it  takes  1  man  6  hours  to  cut  a  cord  of 
wood,  how  long  will  it  take  2  men  to  do  it  ?     How 
long  will  it  take  3  men  ? 

7.  A  man  takes  6  hours  to  cut  a  cord  of  wood, 
cutting  each  stick  into  two  pieces.     How  long  will 
it  take  him  if  he  cuts  each  stick  into  three  pieces-? 
In  each  case  draw  a  stick,  and  mark  where  it  is  cut  ? 


146  ARITHMETIC 

8.  What  number  of  cents  can  you  divide  into 
thirds  and  have  6^  in  each  third  ?    Test  your  answer 
by  making  6  dots  for  each  third,  and  then  counting 
all  your  dots  by  6's.     How  many  6's  ?     How  many 
dots? 

9.  What   number   can  you  divide   into  fourths 
and  have  25  in  each  part?    Into  fifths?    Into  sixths? 

10.  If  one-sixth  of  the  distance  between  Chicago 
and  Springfield  is  29  mi.,  how  far  is  it  between  these 
two  cities  ? 

11.  How  many  weeks  in  1  yr  ?     |  yr.  ?     ^  yr.  ? 
fyr.? 

12.  If  a  boy  earns  16  a  week,  how  much  will  he 
earn  in  J  yr.  ? 

13.  If  a  boy  earns  $  7  a  week  and  it  costs  him  $ 5 
a  week  to  live,  how  much  can  he  save  in  ^  yr.  ? 

14.  What  five  different  coins  make  91  ^  ? 

15.  A  lady  made  6  gal.  of  preserves  and  put  them 
up  in  pint  cans.     How  many  cans  did  she  use  ? 

16.  A  5-lb.  pail  of  butter  costs  90  ^.     At  this  rate 
what  must  I  pay  for  21  Ib.  ? 

17.  How  many  pennies  will  be  required  to  form 
a  square  if  there  are  5  pennies  on  each  side  of  the 
square?     Place  pennies  so  as  to  show  how  many  are 
needed. 

•  18.    A  grocer  has  8  gal.  2  qt.  1  pt.  of  cider  which 
he  divides  equally  among  3  customers.     What  does 


LESSON  68  147 

each  receive  ?     Name  the  quantity  and  the  number. 
What  is  the  unit  ?     How  did  you  find  it  ? 

19.  To  how  many  customers  can  a  milkman  sell 
8  gal.  3  qt.  of  milk,  if  he  sells  5  pt.  to  each  cus- 
tomer? Name  the  quantity  and  the  unit.  What  is 
the  number  ?  How  did  you  find  it  ? 

20.'  A  pole  is  ^  in  the  ground  and  J  in  the  air. 
Draw  the  pole.  If  it  is  4  ft.  in  the  ground,  how 
long  is  the  part  in  the  air  ?  How  long  is  the  pole  ? 

21.  A  pole  is  -|  in  the  air  and  -J  in  the  ground. 
If  the  height  above  ground  is  6  ft.,  how  long  is 
the  pole? 

22.  Two  boys  walk,  one  east  at  the  rate  of  3  mi. 
an  hour,  and  the  other  west,  at  |  that  r;ite.     How 
far  apart  will  they  be  4  hr.  after  they  part  ? 


SECTION  VII 


Lesson  69 

i. 

Memorize  the  sum  of  : 

5 

6 

7 

8 

9 

9 

8 

7 

6 

5 

Add: 

2.  59687796 
1916282647      -37        6687 

3.  53569675 
44944358 

22        37        30       44        51        63        72        81 


2 

4 

1 

6 

,      9 

7 

8 

4 

2 

1 

3 

4 

1 

6 

4 

3 

4 

3 

4 

6 

2 

2 

3 

8 

12 

25 

32 

14 

42 

58 

41 

60 

5.  I  bought  a  coat  for  $12,  and  had  left  a  five- 
dollar  bill  and  2  two-dollar  bills.     How  much  money 
had  I  at  first  ? 

6.  I  bought  a  carriage  for  $61,  paid  $5  for  re- 
pairs, and  sold  it  so  as  to  gain  $8.     What  did  I  sell 


148 


LESSON  69  149 

7.  35        15        48        94        69        46        55        49 

24        77        86        39        72        38        77        80 

8.  234      639      149      475      298      329      758      829 
181        70      673      328      443      872      686      555 

9.  275      654      283      333      206      542      257      426 
453      513      708      325      304      129      509      328 
221      331      544      516      692      783      134      156 

10.  25  years  ago  a  young  man  entered  the  <ti'my 
at  the  age  of  19.     How  old  is  he  now  ? 

11.  In  an  orchard  there  are  96  apple  trees  and 
J  as  many  cherry  trees.     How  many  trees  are  there 
in  the  orchard? 

12.  A  farmer  has  435  sheep  in  one  flock,  322  in 
a  second,  and  239  in  a  third.     How  many  has  he  all 
together  ? 

Subtract : 

784  638  743  801   417   846   931   432 
352  234  561   271  234   395   888   189 


14. 


15.    Mrs.  Ellis  was  24  yr.  old   on  Feb.  19,  and 
Caryl  8.     What  is  the  difference  in  their  ages? 


6465 

9039 

4398 
3489 
8429 

6000 
2009 

7172 

3040 

2361 

1847 

2127 
8666 

1945 
5329 

1321 

4888 

3516 

6354 

1678 

150  ARITHMETIC 

16.  There  are  25  pupils  in  the  second  grade,  and 
16  more  in  the  first.     How  many  are  there  in  both 
grades  ? 

17.  A  boy  rode  75  mi.  on  a  bicycle  in  two  days. 
If  he  rode  49  mi.  the  first  day,  how  far  did  he  ride 
the  second  day  ?     How  many  miles  less  than  on  the 
first  day  ? 

18.  A  farmer  has  165  A.  in  oats,  124  A.  in  barley, 
and  225  A.  in  wheat.      How  many  acres  of  grain 
has  he? 

19.  A  farmer  sold  2  cows  at  $  23  each  and  3  sheep 
at  16.25  apiece.     What  did  he  receive  altogether  ? 

20.  A  farmer  sold  a  grocer  6  T.  of  hay  at  1 12  a 

ton  and  bought  $25.50  worth  of  groceries.     How 
much  cash  did  he  receive  ? 

21.  My  salary  is  $  84  a  month.     I  spend  J  of  this 
for  board,  1  for  clothing,  and  ^  for  other  expenses. 
How  much  do  I  spend  altogether?     How  much  do 
I  save  ? 

22.  Alder  had  24  marbles.      In  the  morning  he 
lost  ^  of  them  and  in  the  afternoon  he  won  |  as  many 
as  he  had  at  noon.     How  many  marbles  had  he  at 
night  ? 

Lesson  70 

1.    Memorize  the  sum  of  :  6789 

9876 


LESSON  70  151 


Add: 

2. 

6 

6 

9 

9 

7 

7 

8 

8 

29 

49 

66 

86 

18 

38 

57 

77 

3. 

9 

4 

5 

6 

7 

8 

3 

8 

4 

4 

5 

6 

7 

8 

7 

7 

22 

34 

45 

66 

77 

88 

92 

16 

4. 

1 

5 

9 

5 

6 

7 

5 

2 

2 

4 

2 

1 

7 

3 

6 

9 

3 

2 

2 

3 

8 

4 

6 

5 

13 

24 

32 

44 

56 

68 

77 

84 

5.  A  man  had  his  life  insured  7  years  ago  when 
he  was  48  yr.  of  age.     How  old  is  he  ? 

6.  A  man  earns  $22.50  a  week,  his  oldest  son 
\  as  much,  and  the  youngest  J  as  much.     What  is 
the  sum  of  their  weekly  earnings  ? 

7.  A  box  weighing  5  Ib.  contains  48  Ib.  of  sugar, 
6  Ib.  of  coffee,  and  3  Ib.  of  tea.     Find  its  entire 
weight. 

8.  29       65       65       86       86       54       43       67 
4674573849369088 

9.  458       29     284     777     506     364     285     789 
203     843     369     666     909     859     367     412. 

10.      34     702     266     280     423     638     215     242 

23     516     315     398       27     399     328     381 

919     370     864     246     392     541     785     899 


152  ARITHMETIC 

11.  Two  men  travel,  one  68  mi.  east  of  Chicago 
and  the  other  47  mi.  west.     How  far  apart  will  they 
be  when  they  reach  their  destination  ?     Draw  a  line 
and  represent  the  three  places  on  this  line. 

12.  Two  men  travel,  one  east  and  the  other  west 
of  Chicago,  the  first  at  the  rate  of  36  mi.  an  hour 
and  the  other  at  the  rate  of  24  mi.  an  hour.     How 
far  apart  will  they  be  in  2  hr.  ? 

Subtract : 

684     647     811     502     824     721     554     921 
13'   253     385     468     341     527     315     379     763 

6724  5289  6903  8000 

14'  3103  4503  4278  3574 

6105  3060  8140  3435 

4239  1432  2352  1547 

15.  One  of  two  farms  contains  384  A.  and  the 
other  is  ^  as  large.      The  first  contains  how  many 
more  acres  than  the  second  ? 

16.  A  man  bought  6  doz.  oranges  at  22^  a  dozen. 
One  dozen  were  spoiled,  and  he  sold  the  rest  at  30^  a 
dozen.     How  much  did  he  gain  ? 

17.  I   sold   a  lot   for  $650,  losing  $275;    what 
should  I  have  sold  it  for  to  gain  $125? 

18.  James  had  $.42.     He  spent  f  of  it  for  a  ball, 
and  5/  for  an  orange.     How  much  had  he  left  ? 


LESSON  71 


153 


19.  I  bought  a  house  and  lot  for  $  4250  and  spent 
11000  on  it  in  repairs.     I  then  sold  it  for  15925. 
What  was  my  gain  ? 

20.  A  laborer  worked  248  days  during  the  year. 
He  worked  how  many  days  more  than  he  was  idle  ? 


Lesson  71 

i.  1x7=  7  7xl  =  ?   5x7  =  35  7x5  =  ? 

2x7  =  14  7x2  =  ?   6x7  =  42  7x6  =  ? 

3x7  =  21  7x3  =  ?  42  +  7=  ?  7x7  =  ? 

4x7  =  28  7x4  =  ?  49  +  7=  ?  8x7  =  ? 

2.  Count  by  7's  from  7  to  84.     Count  by  7's  from 

84  to  7. 


3.    Memorize : 


Seven  times 


lis    7 

5  is  35 

9  is  63 

2  is  14 

6  is  42 

10  is  70 

3  is  21 

7  is  49 

11  is  77 

4  is  28 

8  is  56 

12  is  84 

4.  Give  two  factors  of  each  of  the  following  num- 
bers :  32,  56,  66,  63,  35,  48,  84,  44,  27,  77. 

5.  What  number  is  the  greatest  common  factor  of 
24  and  32  ;  35  and  55  ;  42  and  28  ;  48  and  56 ;  72 

and  84. 


154  ARITHMETIC 

6.  Draw  two   lines,   one  18  in.   and   the   other 
30  in.  long.     What  is  the  longest  line  that  can  be 
used  to  measure  both  lines?     Test  by  measuring. 

7.  Find  the   largest   can   that   can   be   used  to 
measure  the  oil  in  each  of  two  barrels,  one  of  which 
has  20  gal.  and  the  other  25  gal. 

8.  Multiply : 

54        32        63        89        77        99        48 

7          7        JT          7          7          7          7 

In  multiplying  54  by  7  you  carry  2.  This  2  is  2 
what?  In  multiplying  5  by  7  you  get  35.  This  5 
is  5  what  ?  35  is  35  what  ?  35  tens  +  2  tens  =  ? 

9.  456    581    695    945    998    672 

4     5     6     7     7     7 

10.  At  the  rate  of  36  mi.  an  hour,  how  far  will  a 
»rain  run  in  4  hr.  ?      Name  the  unit,  the  number, 
and  the  quantity.     How  did  you  find  the  quantity  ? 
With  the  same  numbers  state  the  question  in  which 
you  have  to  find  the  unit.     Another  in  which  you 
have  to  find  the  number. 

11.  A  lawyer  employs  in  his  office  7  clerks,  and 
pays  them  on  the  average  $456  a  year.     What  is  the 
total  amount  of  their  yearly  salaries  ? 

12.  What  number  smaller  than  20  has  7  for  a 
factor?     Smaller  than  39?    52?    31?    60?    41?    43? 
34?    64?    58?    55? 


LESSON 


155 


13.    Find  the  value  of : 
294  -*-  7         182-7 


511-7 


245-7 


14.  How  many  weeks  and  days   are  there  in  a 
year  of  366  da.  ? 

15.  A  merchant  buys  gloves  at  85^  per  pair,  and 
sells'  them  at  99^  a  pair.     How  much  does  he  gain 
on  8  pairs  if  one  pair  is  damaged  and  is  sold  for  50  ^  ? 

16.  How  many  barrels  of  flour  at  $5  a  barrel  will 
cost  as   much  as  40  bbl.    of  apples  at  $  3  a  bbl.  ? 
Name  the  quantity  and  the  unit.     How  did  you  find 
the  number? 


17.    Harry  bought  7  chickens  at  $  .25  apiece, 
much  had  he  left  out  of  1 2  ? 


How 


18.  Find  the  cost  of  the  following  articles  :  3  2-lb. 
packages  cracked  wheat  at  $.12  each,  7  Ib.  graham 
flour  at  1.03  a  Ib.,  and  1  Ib.  coffee  at  1.35  a  Ib. 


Lesson  72 

1.    Count  by  8's  from   8  to  96. 
from  96  to  8. 


Count  by  8's 


2.    Memorize : 


Eight  times 


1  is     8 

5  is  40 

9  is  72 

2  is  16 

6  is  48 

10  is  8.0 

3  is  24 

7  is  56 

11  is  88 

4  is  32 

8  is  64 

12  is  96 

156  ARITHMETIC 

x 

3.  Find    the   value   of   each   of   the   following: 
8  x  13.05,  8  x35  A.,  8  x  57  lb.,  S  x  88  bu.,  8  x  96  T. 

4.  What  is  the  weight  of  8  25-lb.  sacks  of  .flour 
and  4  50  -lb.  sacks  ? 

5.  Last  year  my  coal  cost  $61.50.     This  year  I 
bought  8  T.  at  $6J  a  ton.     How  much  less  did  my 
coal  cost  this  year  than  last? 

6.  A  lady  bought  8  yd.  of  cloth  at  $ 3|-  a  yard, 
a  hat  for  $8,  and  had  $16  left  in  her  purse.     How 
much  had  she  at  first  ? 

7.  Find    the    value    of:    4x13.15,   5x$8.09, 
6x$2.19,  7x$2.56,  8  x  $3.96. 

8.  How  many  pages  are  there  in  8  arithmetics, 
each  of  which  contains  218  pages? 

9.  A   drover   bought   356    sheep   at  $8   apiece. 
What  did  they  cost  him?     If  he  sold  them  for  $9 
apiece,  what  did  he  gain  ? 

10.  What  is  the  value  of  $1968  ^  8,  $2440  -5-  $8, 
2848  bu.  -j-Sbu.,  6984  bu.  +  8? 

11.  If  1408  A.  is  divided  into  8  farms  of  equal 
size,  how  many  acres  are  there  in  each  farm  ?     Name 
the  quantity,  number,  and  unit. 

12.  An   employer    distributes   $2192   among  his 
workmen,  giving  $8  to  each.     Find  the  number  of 
workmen.     Wha  t  is  the  unit  here  ? 

13.  If  3  lb.  of  sugar  cost  16  £  what  will  24  lb. 
cost  ?     What  is  the  number  here  ? 


LESSON  72  157 


14.  How  long  are  the  lines  a  and  b?     What  part 
of  b  is  equal  to  a  ?     a  is  equal  to  %  of  b.     The  ratio 
of  a  to  b  is  £.     The  ratio  of  b  to  a  is  I-. 

o  .4 

15.  Draw   lines  2   2-in.   long   and  3  2-in.   long. 
What  part  of  the  line  3  2-in.  is  equal  to  the  line 
2  2-in.  ?     2  2-in.  is  what  part  of  3  2-in.  ?     What  is 
the  ratio  of  2  2-in.  to  3  2-in.  ?     Of  3  2-in.  to  2  2-in.  ? 


16.  What  is  the  ratio  of  2  2-dots  to  3  2-dots? 
Of  3  2-dots  to  2  2-dots?     What  is  the  ratio  of  the 
weight  of  2  2-lb.  rolls  of  butter  to  that  of  3  2-lb. 
rolls?     Of  the  cost? 

17.  If  3  2-lb.  rolls  of  butter  cost  90  ^,  what  will 
2  2-lb.  rolls  cost? 

18.  What  is  the  ratio  of  the  cost  of  3  2-lb.  of 
butter  to  that  of  2  2-lb.  ?     If  2  2-lb.  rolls  of  butter 
cost  48^,  what  will  3  2-lb.  rolls  cost? 

19.  What  is  the  largest  unit  that  measures  4  in. 
and  6  in.  ?     How  often  in  each  case  ?     What  is  the 
ratio  of  4  in.  to  6  in.  ?     Of  6  in.  to  4  in.  ? 

20.  What  is  the  ratio  of  4  yd.  to  6  yd.  ?     Of  6  yd. 
to  4  yd.  ?     Of  the  cost  of  4  yd.  of  ribbon  to  the  cost 


158  ARITHMETIC 

of  6  yd.?     If  6  yd.  of  ribbon  cost  $.63,  what  will 

4  yd.  cost? 

21.  What  is  the  ratio  of  4  f  to  6  f  ?     Of  $4  to  1 6  ? 
Of  6^  to  4^?     Of  $6  to  14?     Of  the  amount  $4 
will  buy  to  that  which  $6  will  buy?     If  $4  will  buy 

5  gal.  of  maple  syrup,  how  many  quarts  will  $6  buy? 

22.  What  is  the  largest  unit  that  measures  6  in. 
and  8  in.  ?     6  in.  =  ?  2-in.     8  in.  =  ?  2-in.     What 
is  the  ratio  of  6  in.  to  8  in.  ?     Of  8  in.  to  6  in.  ?     Of 

6  ft.  to  8  ft.?     Of  8  yd.  to  6  yd.?     Of  §4  to  8^? 
Of  8  dimes  to  6  dimes  ? 

23.  At  6  boxes  for  33^,  what  will  8  boxes  of  ber- 
ries cost?     At  8^  for  |-  pk.  of  apples,  how  many 
quarts  of  apples  can  you  buy  for  6^? 

24.  James  caught  a  ball  6  times  out  of  8.     How 
many  times  did  he  miss  it  in  96  chances? 

Lesson  73 

1.  Fill  a  peck  measure  with  a  quart  measure. 
How  many  quarts  in  one  peck  ?     1  pk.  =  ?  qt. 

2.  Fill  a  bushel  measure  with  a  peck  measure. 
How  many  pecks  in  one  bushel?     How  many  quarts 
in  one  bushel?     ?  pt.  =1  qt.     ?  qt.  =1  pk.     ?  pk.  = 
1  bu.     1  bu.  =  ?  qt. 

'  3.    3  pk.  =  ?  qt.       6  pk.  =  ?  qt.       4  pk.  =  ?  qt. 
5  pk.  =  ?  qt.       8  pk.  =  ?  qt.       9"  pk.  =  ?  qt. 
How  can  you  reduce  pecks  to  quarts  without  actu- 
ally measuring  ? 


LESSON  n 

4.  Reduce  to  quarts :   2  pk.  3  qt.  ;   5  pk.  6  qt. ; 
7  pk.  4  qt.  ;   1  bu.  ;  3  bu. ;   5  bu.  4  qt. 

How  do  you  reduce  bushels  to  quarts  ? 

5.  11  bu.  =  ?  qt.    3J-  bu.  =  ?  qt.    2J  bu.  =  ?  qt. 
21  pk.  =  ?  qt.    3f  pk.  =  ?  qt. 

6.  2  bu.  3  pk.  =  ?  pk.     2  bu.  3  pk.  4  qt.  =  ?  qt. 
3  bu.  2  pk.  4  qt  =  ?  qt.     4  bu.  3  qt.  =  ?  qt. 

7.  A  bushel  of  oats  weighs  32  Ib.     What  does 
1  qt.  of  oats  weigh?     1  pk.  ? 

What  is  the  weight  of  2  bu.  3  pk.  6  qt.  of  oats? 

8.  What  part  of  a  bushel  is  2  pk.  ? 

A  bushel  of   beans  weighs  60  Ib.     What  is  the 
weight  of  3  bu.  2  pk.  ? 

9.  15  pk.  =  ?  bu.  pk.        25  pk.  =  ?  bu.  pk. 
30  qt.  =  ?  pk.  qt.         18  qt.  =  ?  pk.  qt. 

10.  36  qt.  =  ?  bu.     18  pk.  =  ?  bu.     48  qt.  =  ?  bu. 
What  is  the  cost  of  48  qt.  of  potatoes  at  60  f  a  bu.  ? 

11.  What  is  the  weight  of  40  qt.  of  wheat  if  1  bu, 
weighs  60  Ib.  ? 

12.  How  many  ounces  are  there  in  1  Ib.  of  butter9 
Name  other  articles,  one  pound  of  which  contains  16 
oz.     How  could  such  an  expression  as  2  Ib.  6  oz. 
arise  ? 

13.  1 J  Ib.  =  ?  oz.      2f  Ib.  =  ?  oz.      3f  Ib.  =  ?  oz 
4  oz.   =  ?  Ib.      8  oz.    =  ?  Ib.      12  oz.  =  ?  Ib 
1  oz.   =  ?  Ib.      2  oz.    =  ?  Ib.       5  oz.  =  ?  Ib. 


160  ARITHMETIC 

14.  What  is  the   price   of  pepper  per  oz.   when 
|lb.  costs  8^? 

15.  What  is  the  weight  in  ounces  of  5  J-lb.  cans 
of  mustard,  3  J-lb.  cans,  and  2  1-lb.  cans  ? 

16.  3  Ib.  4  oz.  =  ?  oz.     4  Ib.  6  oz.  =  ?  oz.     At 
$  .16  a  Ib.  what  is  the  cost  of  5  Ib.  8  oz.  of  butter? 

Lesson  74 

1.  Place  cubic  inches,  making  a  pile  4  in.  long, 
3  in.  wide,  2  in.  thick.     Count  their  number  thus : 
One  3-cu.  in,  two  3-cu.  in.,  i.e.  6  cu.  in.  (2x3  =  6). 
One   6-cu.   in.,  two  6-cu.  in.,  three  6-cu.   in.,  four 
6-cu.  in.,  i.e.  24  cu.  in.  (4x6  =  24).     The  volume  = 
24  cu.  in. 

2.  How  can  you  get  the  number  24  in  question  1 
without  counting?     What  is  the  unit? 

3.  How  many  cubic  inches  in  a  prism  2  in.  long, 
1  in.  wide,  and  1  in.  thick  ?     Make  this  prism. 

4.  Find  the  number  of  cubic  inches  in  each  of 
the  following  prisms,  the  dimensions  being  given  in 
inches  : 

Length       Width       Thickness  Length       Width       Thickness 

311  642 

321  633 

432  843 

653  864 


LESSON  74  161 

How  do  you  find  the  number  of  cubic  inches  in  a 
prism  ? 

5.  What  is  the  volume  of  a  1-in.  cube?     2-in. 
cube?     3-iu.  cube?     4-in.  cube?     5-in.  cube?     6-in. 
cube?     7-in.  cube?     8-in.  cube? 

6.  A  2-in.  cube  can  be  cut  into  how  many  1-in. 
cubes?      A  4-in.  cube  can  be  cut  into  how  many 
2-in.   cubes?      What  is   the  unit   of   length   here? 
The  unit  of  volume? 

7.  An  8-in.  cube  can  be  cut  into  how  many  4-in. 
cubes  ?     How  many  2-in.  cubes  ?     What  is  the  unit 
of  volume  here  ? 

8.  A  6-in.  cube  can  be  cut  into  how  many  3-in. 
cubes?     How  many  2-in.  cubes? 

9.  Measure   and   find  the   volume   of   as   many 
prisms  as  you  can  find. 

10.  Mark  off  and  build  up  in  the  corner  of  the 
room  one  cubic  foot. 

11.  What  is  the  volume  of  a  prism  8  in.  long, 
4  in.  wide,  and  4  in.  high? 

12.  What  is  the  volume  of  a  pile  of  wood  8  ft.  long, 
4  ft.  wide,  and  4  ft.  high?     How  do  you  find  the 
number  of  units  of  volume  in  any  prism? 

13.  A  pile  of  wood  8  ft.  long,  4  ft.  wide,  and  4  ft. 
high  is  called  a  cord.     Mark  off  a  cord  in  the  corner 
of  the  room  ?     What  is  sold  by  the  cord  ? 

M 


ARITHMETIC  ' 

14.  How  many  cubic  feet  are  there  in  a  box  3  ft. 
long,  1  ft.  wide,  and  1  ft.  deep? 

15.  How  many  cubic  feet  are  there  in  a  box  3  ft. 
long,  3  ft.  wide,  and  2  ft.  deep?     4  ft.  long,  3  ft. 
wide,  and  2  J  ft.  deep  ? 

16.  How  many  3-in.  cubes  could  be  placed  in  a 
box  3  ft.  long,  2  ft.  6  in.  wide,  and  1  ft.  6  in.  deep? 

17.  How  many  cubic  inches  in  a  tin  box  11  in. 
long,  7  in.  wide,  and  3  in.  deep?     Such  a  box  will 
hold  exactly  a  gallon.     Pour  a  gallon  of  water  into 
such  a  box  and  prove  this.     1  gal.  =  ?  cu.  in. 

18.  A  cubic  foot  of  water  weighs  1000  oz.     A  tank 
4  ft.  long,  2  ft.  wide,  and  1  ft.  deep  is  full  of  water. 
How  many  ounces  does  it  weigh? 

19.  What  is  the  weight  of  a  block  of  stone  6  in. 
long,  4  in.  wide,  and  2  in.  thick,  if  8  cu.  in.  weigh 
1  Ib.  ? 

20.  How  many  square   inches   are  there  on  the 
surface  of  a  cube  whose  edge  is  4  in.  ? 

21.  Measure  the  dimensions  of  several  boxes  and 
find  their  volumes. 


SECTION  VIII 

Lesson  75 

1.  In  the  Roman  notation  numbers  are  expressed 
by  means  of  seven  capital  letters.     These  letters  are 
used  to  denote  numbers,  and  their  values  are  written 
in  question  2.     This  is  called  the  Roman  notation 
because  the  Romans  were  the  first  to  use  these  letters 
for  this  purpose. 

2.  I.         V.         X.         L.         C.          D.          M. 

1.         5.         10.        50.      100.       500.       1000. 

3.  VI  (V  + 1)  =  6  VIII  (V  +  HI)  =  8 
XV  (X  +  V)  =  15       XX  (X  +  X)  =  20. 

4.  Write  in  Roman  notation  6,  7,  8  ;  15, 16, 17, 18. 

5.  Write  in  Roman  notation  20,  21,  22,  23 ;  25, 

26,  27,  28. 

6.  Write  in  Roman  notation  30,  31,  32,  33;  35, 

36,  37,  38. 

7.  Write  in  Roman  notation  50,  51,  52,  53 ;  55, 

56,  57,  58. 

8.  IV  (V  -  I)  =  4          IX  (X  -  I)  =  9 
XL  (L  -  X)  =  40      XC  (C  -  X)  =  90. 

163 


164  ARITHMETIC 

9.    Write  in  Roman  notation  4,  14 ;  20,  24  ;  30, 
34;  40,44;  50,  54. 

10.  Write  in  Roman  notation  9,  19,  29,  39,  49,  59, 

69,  79,  89. 

11.  Write  in  Roman  notation  90,  91,  94,  95,  97, 
99,  100. 

12.  Look   at  the   clock  face,  in   the   prefaces  of 
books,  at  the  beginning  of   chapters  or  sections  of 
books,  and  find  out  where  Roman  numerals  are  used. 

Study  the  following  carefully : 


13.           1=     1 

XI  =  11 

?  =  21 

11=    2 

XII  =  12 

?  =  22 

111=    3 

XIII  =  13 

?  =  23 

IV  =    4 

XIV  =  14 

?  =  24 

V=    5 

XV  =  15 

?  =  25 

VI  =    6 

XVI  =  16 

?  =  26 

VII  =    7 

XVII  =  17 

?  =  27 

VIII  =    8 

XVIII  =  18 

?  =  28 

IX  =    9 

XIX  =  19 

?  =  29 

X  =  10 

XX  =  20 

?  =  30 

14.    XL  =  40 

XC=    90 

D=    500 

L  =  50 

0  =  100 

DC=    600 

LX  =  60 

CXXX  =  130 

DCC=    700 

LXX  =  70 

CCC  =  300 

M  =  1000 

15.    Write  in  Roman  numerals  the  numbers  from 
30  to  100. 


LESSON  76  165 

16.  Write  in  Roman  numerals  110,  140,  149,  150, 
154,  182,  190,  194. 

17.  Write  in  Roman  numerals  300,  15,  315  ;  200, 
84,  284  ;  500,  99,  599 ;  614,  739,  827,  934. 

18.  Write  in  Roman  numerals  1000,  250,  1250; 
344,  1344,  1898,  1492. 

19.  Read,  and  write  the  numbers  in  figures  : 

(a)  Henry  Hudson  discovered  the  Hudson  River 
in  MDCIX. 

(6)  The  Pilgrims  landed  in  MDCXX. 

(c)  Georgia  was  settled  in  MDCCXXXIL 

(cT)  The  battle  of  Bunker  Hill  was  fought  in 
MDCCLXXV. 

(e)  The  World's  Fair  was  held  in  Chicago  in 
MDCCCXCIII. 

Lesson  76 

1.  Review  the  multiplication  tables  of  7  and  8. 

2.  Write  down  one-seventh  of  $14,  $28,  $35, 
$56,  $70.     Write  down  three-sevenths  of  $14,  $28, 
$  35,  $  56,  $  70.     How  do  you  find  one-seventh  of  a 
quantity  ?     Three-sevenths  ? 

3.  A  man's  salary  was  $42  a  week,  and  his  ex- 
penses £  of  his  salary.     How  much  did  he  save  each 
week? 

4.  Write  down  one-eighth  of  $  16,  $  24,  $  32,  $  64, 
Write  down  five-eighths  of  $16,  $24,  $32, 


166  ARITHMETIC 

$64,  $  96.     How  do  you  find  one-eighth  of  a  quantity  ? 
Five-eighths  ? 

5.  A  lady  had  $40,  and  .spent  |  of  it  for  groceries. 
With  the  remainder  she  bought  a  wrap.     What  did 
the  wrap  cost  ? 

6.  My  expenses  in  one  month  were  $  56;  I  spent  | 
of  it  for  board,  ^  of  it  for  a  suit  of  clothes,  and  the 
remainder  for  an  overcoat.     What  did  I  spend  for 
each  item  ? 

7.  A  grocer  paid  $  .60  a  bu.  for  potatoes,  and  sold 
them  for  20^  a  pk.     What  did  he  gain  per  bu.? 

8.  Which  will  cost  more,  J  pk.  of  apples  at  24  $  a 
pk.  or  |  pk.  of  potatoes  at  15^  a  pk.  ?     How  much? 

9.  A  man  saved  ^  of  his  salary.     What  part  of 
his  salary  did  he  spend?     If  he  had  spent  |  of  his 
salary,  what  part  of  it  would  he  have  saved  ? 

10.  A  watch  cost  7  times  as  much  as  the  chain. 
The  cost  of  both  was  how  many  times  the  cost  of  the 
chain  ?     What  do  you  take  as  the  unit  of  measure  ? 

11.  If  the  watch  and  chain  in  question  10  together 
cost  $  80,  what  was  the  cost  of  the  chain  ?     Of  the 
watch  ? 

12.  |  of  $24    =?    |of$20     =?     fof$32    =? 
f  of  20  Ib.  =  ?     |  of  10  Ib.  =  ?     |  of  30  Ib.  =  ? 

13.  f of  18 gal.  =  ?    fof28gal.=?    fof21gal.=? 

40yd.=?    |of56yd.  =?    £of24yd.  =? 


LESSON  76  167 

14.  A   lady  bought  a  piece  of   cloth  containing 
18  yd.     She  required  J  of  it  for  a  dress  for  herself 
and  J  as  much  for  her  daughter.     How  many  yards 
were  in  each  dress  ?     How  much  was  left  over  ? 

15.  What  is  the  ratio  of  4  ft.  to  8  ft.  ?     Of  8  ft. 
to  4  ft.  ?      1  yd.  1  f t.  =  ?  ft.      2  yd.  2  ft.  =  ?  ft. 
What  is  the  ratio  of  1  yd.  1  ft.  to  2  yd.  2  ft-?     Of 
2  yd.  2  ft.  to  1  yd.  1  ft.  ?     Draw  lines  1  yd.   1  ft. 
long  and  2  yd.   2  ft.   long  and  prove  your  result 
correct. 

16.  If  2  yd.  2  ft.  of  cloth  cost  96^,  what  part  of 
96  ^  will  a  piece  1  yd.  1  ft.  long  cost  ?     How  much  ? 

17.  How  many  ft.  in  2  yd.  1  ft.?    In  7  yd.?    What 
is  the  ratio  of  2  yd.  1  ft.  to  7  yd.  ?     Of  the  cost  of 
2  yd.  1  ft.  to  that  of  7  yd.  ? 

18.  If  7  yd.  of  ribbon  cost  84  £  what  will  2  yd. 
1  ft.  cost  ? 

19.  How  many  pints  in  2  qt.  1  pt.  ?    In  7  qt.  1  pt.  ? 
What  is  the  ratio  of  2  qt.  1  pt.  to  7  qt.  1  pt.  ?     Of 
7  qt.  1  pt.  to  2  qt.  1  pt.  ? 

20.  If  2  qt.  1  pt.   of  milk  cost  f  .15,  what  will 
7  qt.  1  pt.  cost? 

A  milkman  sells  2  qt.  1  pt.  of  milk  to  each  of 
three  customers.     How  much  do  they  all  buy  ? 

21.  How  many  quarts  in  2  gal.  1  qt.  ?     If  2  gal. 
1  qt.  of  oil  cost  18  f,  what  will  9  gal.  cost  ?    If  6  gal, 


168  ARITHMETIC 

3  qt.  of  maple  syrup  cost  f  6,  what  will  2  gal.  1  qt. 
cost? 

22.  What  is  the  ratio  of  2  bu.  1  pk.  to  11  bu. 
1  pk.  ?     Of  11  bu.  1  pk.  to  2  bu.  1  pk.?     If  2  bu. 

I  pk.  of  barley  weigh  108  lb.,  what  will  11  bu.  1  pk. 
-reigh? 

23.  If  2  bu.  1  pk.  of  oats  weigh  72  lb.,  what  will 

II  bu.  1  pk.  cost  at  1  f  a  lb.  ? 

24.  If  an  express  train  runs  45  mi.  in  1  hr.  30  min., 
far  will  it  run  in  3  hr.  at  the  same  rate  ? 

Lesson  77 


•     •     • 

1.    Let  each  dot  represent  1  ^.     1  f  is  what  part 
of  6^?     2^  is  what  part?     3^?     4^?     5^? 


2.  Let  each  dot  represent  1  lb.     2  lb.  is  what 
part  of  8  lb.?    4  lb.  ?     6  lb.  ?     7  lb.  ?     8  lb.  ? 

3.  1  lb.  +  3  lb.  =  ?  lb.     The  sum  of  1  lb.  and 

3  lb.  is  what  part  of  8  lb.  ?     The  sum  of  2  lb.  and 

4  lb.  is  what  part  of  8  lb.  ? 

4.  From  a  piece  of  ribbon  8  yd.  long  were  sold 
2  yd.  to  each  of  2  customers.     The  part  sold  was 
what  part  of  the  original  piece  ? 


LESSON  77  169 

5.  £  ft.  +  I  ft.  =  ?      1  ft,  +  |  ft.  =  ?      f  ft.  +  f  ft.  =  ? 
lft.+fft.  =  ?      fft.+flt.=?      fft.+£ft.=? 

6.  Find  the  sum  of  ^  ft.  and  J  ft.     Why  can  you 
not  find  the  sum  of  ^  ft.  and  J  ft.  as  you  found  the 
sum  of  J  ft.  and  |  ft.  ?     How  can  you  find  their  sum  ? 

7.  Draw  a  line  1  ft.  long,  and  divide  it  into  6 
equal  parts.     Mark  off  on  this  line  parts  ^  ft.  and 
^  ft.  long.     Their  sum  is  what  part  of  1  ft.  ?     Their 
difference  is  what  part?     Into  how  many  units  was 
1  ft.  divided? 


8.  If  these  6  dots  represent  1  ft.,  what  part  of  a 
foot  is  represented  by  2  dots,  by  3  dots,  by  4  dots,  by 
5  dots,  by  6  dots  ? 

9.  If  these  6  dots  represent  1  ft.,  how  many  dots 
represent  1  ft?     1  ft.?     Their  sum?     This  is  what 
part  of   a   foot?      How  many  dots  represent  their 
difference  ?     This  is  what  part  of  a  foot  ?    |-  f  t.  +  ^  ft. 
=  fft.     £ft.+£ft.  =  ?     1ft.  -lft.=lft. 

10.  What  is  the  sum  of  |  yd.  and  1  yd.  ?     What 
is  their  difference?     Draw  a  line  1  yd.  long,  mark  it 
off  into  parts  as  in  question  7,  and  prove  your  answers 
correct.     Into  how  many  units  was  1  yd.  divided? 

11.  i  da.  -  i  da.  =  ?  l  da.  +  1  da.  =  ? 
|  hr.  -  |  hr.  =  ?             1  hr.  +  £  hr.  =  ? 
1  bu.  +  1  bu.  =  ?  \  bu.  -  l  bu.  =  ? 

f  yr.  +  £  yr.  =  ? 


170  AKITHMETIC 

12.  What  is  the  sum  of  one-half  of  a  quantity  and 
one-third  of  it?     Of  one-third  of  a  quantity  and  one- 

lalf  of  it?     What  is  the  difference  between  one-half 
of  a  quantity  and  one-third  of  it  ? 

13.  A  young  man  spent  J  of  his  weekly  salary  for 
board,  J  of  it  for  clothing,  and  the  rest  he  saved. 
What  part  of  his  salary  did  he  spend?     What  part 
did  he  save  ?     If  he  saved  $  2,  what  was  his  weekly 
salary  ? 

14.  A  man  left  J  his  money  to  his  wife,  and  J  to 
his  oldest  son.     What  was  the  difference  between 
their  shares?     If  this  was  §3000,  how  much  money 
was  left? 


15.  If  these  8  dots  represent  1  gal.,  mark  off  by 
a  line  the  number  of  dots  that  represent  f  gal.  and 
^  gal.     How  many  represent  their  sum?     This  is 
what  part  of  a  gallon?     Their  difference?     This  is 
what  part  of  a  gallon? 

f  gal-  -  i  gal.  =  ?  gal.        f  gal.  +  J  gal.  =  ?  gal. 

16.  How  many  pints  in  1  gal.  ?     In  |  gal.  ?     In- 
^  gal.  ?     In  the  difference  between  f  gal.  and  J  gal.  ? 
This  is  what  part  of  a  gallon  ?     How  many  pints  in 
their  sum?     This  is  what  part  of  a  gallon? 

17.  Into  a  pitcher  containing  |  gal.  of  water  there 
is  poured  ^  gal.     How  many  pints  are  there  in  the 
pitcher  ?     There  is  what  part  of  a  gallon  ? 


LESSON  77  171 

18.  What  is  the  sum  of  f  of  a  man's  salary  and 
J  of  it?     The  difference? 

What  part  of  a  year  is  gone  when  J  and  |-  of  it 
are  gone?  What  is  the  sum  of  one-fourth  and 
three-eighths  of  a  quantity?  What  is  the  differ- 
ence? 

19.  Using  the  8  dots  in  question  15  to  represent 
$1,  find  the  sum  of  $1,  f  £,  ||. 


Place  8  dots  in  each  case,  and  mark  off  the  dots 
that  represent  the  fractions  in  each  question. 

20.    By  how  many  dots  or  units  will  you  represent 
one  dollar  in  the  following  questions  ? 


21.  What   is  the  weight  of  a  parcel  containing 
J  Ib.  of  candy  and  |  Ib.  of  figs? 

22.  James  is  £  and  his  brother  Arthur  ^  of  their 
father's  age.     If  the  difference  in  their  ages  is  5  yr., 
how  old  is  their  father? 

23.  When  you  found  in  question  9  the  sum  of 
J  ft.  and  J  ft.,  by  how  many  dots  or  units  did  you 
represent  1  ft.  ?     How  is  6  related  to  2  and  3  ?     If 
you  were  adding  £  ft.  and  ^  ft.,  into  how  many  parts 
or  units  would  you  represent  1  ft.  as  being  divided  ? 
How  is  this  number  related  to  3  and  4?. 


172  ARITHMETIC 

24.  Place  12  dots  to  represent  1  ft.,  and  mark  off 
the  number  representing  |  ft.  and  ^  ft.  -J-  ft.  = 
?  dots.  -J  ft.  =  ?  dots.  J  ft.  +  J  ft.  =  ?  dots.  This 
is  what  part  of  a  foot  ? 

Lesson  78 

1.  In  each  of  the  following  cases,  into  how  many 
parts   do   you   think   of   $1,   1   lb.,   etc.,   as   being 
divided  ? 

When  you  add  $J  and  $|;  J  lb.  and  f  lb.  ;  $  J 
and  9&  ;  f  lb.  and  •&  lb.  ;  £  yd.  and  £  yd.  ;  f  yd. 
and  |  yd.  ;  f  gal.  and  £  gal.  ;  £  A.  and  1  A.  ? 

2.  In  each  of  the  following  questions  represent 
1  lb.  by  dots,  and  mark  off  the  number  of  dots  that 
represent  the  parts  of  1  lb.  : 

1  lb.  +  %  lb.  =  ?     j-  lb.  -  |  lb.  =  ?    i-  lb.  +  f  lb.  =  ? 
Jlb.-flb.  =  ?    flb.-|lb.  =  ?    flb.-ilb.=? 

3.  If  Caryl  had  ^  lb.  of  candy,  and  gave  %  lb. 
away,  how  much  did  she  keep  for  herself?     What 
did  her  candy  cost  at  25^  a  lb.? 

4-    i  gal.  +  t  gal.  =  ?        J  gal.  -  1  gal.  =? 
fgal.+igal.=?      i  +  i+A  =  ?     A_i  +  i  =  ? 

5.  What  is  the  cost  of  1  lb.  of  baking  powder  at 
If  a  lb.,  and  2  lb.  butter  at  f  £  a  lb.?  How  many 
cents?  What  change  should  be  given  back  out  of 
a  dollar  bill  ? 


LESSON  78  173 

6.  In  terms  of  what  unit  do  you  express  3  nickels 
and  2  dimes  before  you  can  add  them?     1  yd.  and 
1  ft.  ?      2  ft.  4  in.  and  J  ft.  ?      3  gal.  and  2  qt.  ? 
One-quarter  dollar  and  3  dimes? 

7.  In  terms  of  what  unit  do  you  express  ^  ft. 
and  ^  ft.  before  you  can  add  them? 

(This  unit  is  one-sixth  of  a  foot.) 
^  f t.  =  ?  sixths  of  a  foot.     J  =  how  many  sixths  of 
a  foot?     1  ft.  +  1  ft.  =?      i  ft.  -  1  ft.  =  ? 

8.  In  terms  of  what  unit  do  you  express  ^  yd.  and 
\  yd.  before  you  can  add  them  ?     J  yd.  =  ?  twelfths 
of  a  yard.     ^  yd.  =  ?  twelfths  of  a  yard. 

f  yd.  +  J  yd.  =  ?  §  yd.  -  \  yd.  =  ? 

9.  Why  can  you  not  add  two  fractions  without 
changing  them  to  the  same  unit  ?     Reduce  J,  ^,  and 
J  to  sixths  ? 

10.  Reduce  these  fractions  to  12ths :  J,  £,  f ,  -^,  f , 
J,  f .     How  did  you  reduce  J  to  12ths  ?     f  ?     f  ? 

11.  Reduce  these  fractions  to  lOths :  %,  -J,  f ,  f ,  -f, 
f .     How  did  you  reduce  l  to  lOths  ?     |  ?     |?     |  ? 

12.  A  piece  of  land  containing  %  A.  is  divided 
into  lots  each  containing  ^  A.     Find  the  number  of 
lots. 

13.  Reduce  these  fractions  to  8ths :  J,  ^,  -|,  £. 

14.  A  piece  of  ribbon  |  yd.  long  is  divided  into 
pieces  each  ^  yd.  long.     How  many  pieces? 


174  ARITHMETIC 

15.    What  is  meant  by  the  sum  of  \  and  J?     Find 
the  sum  of : 


^  and  ^ 

f  and  f 

f  and  f 

|and£ 
^  and  f 
f  and  J 

21  and  l 
1  and  If 
2£  and  3f 

f  and  f 
31  and  4 
If  and  T7 

16.  What  is  meant  by  the  difference  between  | 
and  J  ?     Find  the  difference  between  : 

|  and  1  -£  and  f  3£  and  If 

|  and  |  i  and  ^  5T^  and  21 

|  and  I  |  and  f  4^  and  2^ 

f  and  f  2f  and  ^  3^  and  1£ 

17.  How  do  you  find  the  sum  of  two  fractions  ? 
The  difference? 

18.  From  a  piece  of  land  containing  3£  A.,  the 
owner  sells  2J  A.     How  much  has  he  left? 

19.  Mr.   Ellis  gave  Alder  a  five-dollar  bill  with 
which   to   buy  a   hat  that  cost  $2£.      How  much 
change  should  Alder  return  to  his  father  ? 

20.  Daisy  gave  f  5J  for  a  pair  of  shoes,  and  f  16 J 
for  a  jacket.     How  much  had  she  left  from  1 25? 

21.  Draw  three  lines  each  1  ft.  long.     Divide  the 
first  into  2  equal  parts,  the  second  into  4  equal  parts, 
and  the  third  into  6  equal  parts. 

£  ft.  =  ?  in.  f  ft.  =  ?  in.  f  ft.  =  ?  in. 

Which  is  greater,  \  ft.,  £  ft.,  or  f  ft.  ? 


LESSON  79  175 

22.  Find  the  number  of   inches  in  J  yd.,  %  yd., 
and  |  yd.     Which  is  greater,  J  yd.,  %  yd.,  or  f  yd. 

Find  the  number  of  hours  in  ^  da.,  %  da.,  |  da., 
and  |  da.  Which  is  greater,  %  da.,  f  da.,  f  da.,  or 
|da. 

23.  What  is  meant  by  saying  that  J,  -|,  |,  and  -| 
are  equal  ? 

24.  Is  J  also  equal  to  T5¥  or  -^?    Test  by  finding 
the  number  of  minutes  in  J  hr.,  -fa  hr.,  and  -^  hr. 

25.  Show  that  £  bu.  of  oats  is  equal  to  f  or  f  or 
T%  or  if  °^  it.     (1  bu.  oats  weighs  32  Ib.) 

i  =  f  =  t  =  T86=M'  i  =  t  =  T50=A- 

26.  Show  that  J=f  =  f  and  that  i=|=^L. 

Lesson  79 

1.  A  young  man  spent  \  of  his  weekly  salary  for 
board  and  \  of  it  to  meet  other  expenses.     What  part 
of  his  salary  did  he  spend?     What  part  did  he  save? 
If  this  was  f  1.50,  what  was  his  salary? 

2.  What  is  the  difference  between  ^  of  a  quantity 
and  \  of  it  ?     If  the  difference  between  J  of  my  age 
and  \  of  it  is  2  years,  how  old  am  I  ? 

3.  If  three-fourths  of  a  yard  of  ribbon  cost  15^, 
what  will  one-fourth  of  a  yard  cost?     What  will  a 
yard  cost? 

If  f  yd.  of  cloth  cost  24^,  what  will  \  yd.  cost? 

lyd.? 


176  ARITHMETIC 

4.  l  a  field  is  planted  with  potatoes  and  ^  of  it 
with  carrots.     What  part  of  the  field  is  planted  with 
these  two  vegetables  ?     Draw  the  field. 

5.  I  invest  ^  of  my  money  in  a  house  and  lot  and 
|-  of  it  in  business.     This  is  what  part  of  my  money  ? 
What  part  is  left?     If  I  have  $600  left,  how  much 
had  I  at  first? 

6.  Draw  the  farm  in  question  7  ;  divide  it  into  15 
equal  parts  ;  mark  off  the  parts  sold  to  each,  and  also 
the  remainder.     Then  mark  the  number  of  acres  in 
each  part  sold. 

7.  The  owner  of  a  farm  sells  f  of  it  to  one  man 
and  ^  of  it  to  another.     What  part  of  it  does  he  sell  ? 
What  part  does  he  keep  ?     If  this  is  10  A.,  how  large 
was  his  farm  ? 

8.  What  is  the  difference  between  £  of  a  school 

o 

term  and  J  of  it?     If  the  difference  is  10  da.,  how 
many  days  are  there  in  the  school  term  ? 


9.  If  5  of  these  dots  represent  40^,  what  will  1 
dot  represent?  What  will  6  dots  represent?  If 
these  6  dots  represent  the  cost  of  1  yd.  of  cloth,  what 
will  5  dots  represent  ?  1  dot  ?  6  dots  ? 

10.  f  yd.  of  cloth  costs  40  £ 

J  yd.  of  cloth  costs  ? 
&  yd.  of  cloth  costs  ? 
1  yd.  of  cloth  costs  ? 


LESSON  79  177 


11.  £  A.  of  land  costs 

^  A.  of  land  costs  ? 
-|  A.  of  land  costs  ? 
1  A.  costs  ? 

12.  If  |  of  my  weekly  salary  is  $20,  what  is  my 
salary  ? 

13.  A  cask  that  is  f  full  contains  24  gal.;  find  the 
number  of  gallons   it  holds.     Draw  the   cask,  and 
mark  off  the  parts. 

14.  A  man  divided  his  farm  among  his  three  sons. 
The  oldest  got  -|  of  it,  and  the  second  \.      What 
part  of  the  farm  did  these  two  get  ?      What  was 
the  share  of  the  youngest? 

15.  If  the  youngest  son  got  90  A.,  what  was  the 
size  of  the  farm?     How  many  acres  did  each  son  get? 

16.  A  gallon  measure  is  half  full.     If  I  pour  out 
^  gal.,  what  part  of  a  gallon  is  left  in  the  measure  ? 

17.  A  boy  gave  \  of  his  marbles  to  one  boy  and  \ 
to  another.     What  part  of  them  did  he  give  away? 
What  part  did  he  keep? 

18.  A  man  spent  f  of  his  money  for  clothes  and  ^ 
for  a  hat.     What  part  of  it  did  he  spend?     What 
part  did  he  have  left?     If  this  is  $9,  how  much  had 
he  at  first  ? 


SECTION   IX 


Lesson  80 

UNITS  OF  VALUE 
United  States  Money 

10  cents  (ct.  or  ^)  =  1  dime  (d.) 
10  dimes 


Gill 


Pint 


Quart  Gallon 

UNITS  OF  CAPACITY 
Liquid  Measure 

4  gills  (gi.)=l  pint  (pt.) 
2  pints         =  1  quart  (qt.) 
4  quarts       =  1  gallon  (gal.) 


Pint  Quart  peck 

Dry  Measure 

2  pints  (pt.)  =  1  quart  (qt.) 

8  quarts  =  1  peck  (pk.) 

4  pecks,  or  32  quarts  =  1  bushel  (bu.) 
178 


LESSON  80  '    179 

UNITS  OF  WEIGHT 


Avoirdupois    Weight 

16  ounces  (oz.)  =  1  pound  (lb.) 

100  pounds  =  1  hundredweight  (cwt.) 

2000  pounds,  or  20  hundredweight  =  1  ton  (T.) 

UNITS  OF  LENGTH 

Long  Measure 

12  inches  (in.)  =  1  foot  (ft.) 

3  feet  =  1  yard  (yd.) 

5£  yards,  or  16^  feet  =  1  rod  (rd.) 
320  rods    > 

1760  yards  >  =1  mile  (mi.) 

5280  feet    ) 

Measure  in  the  schoolroom  two  points  one  rod  apart. 
Name  two  places  one  mile  apart. 

UNITS  OF  SURFACE 

Surface,  or  Square  Measure 

144  square  inches  (sq.  in.)—  1  square  foot  (sq.  ft.) 
9  square  feet  =  1  square  yard  (sq.  yd.) 

30£  square  yards  =  1  square  rod  (sq.  rd.) 

160  square  rods  =  1  acre  (A.) 

640  acres  =  1  square  mile  (sq.  mi.) 

A  township  is  6  mi.  square  and  contains  36  sq.  ini. 


180  ARITHMETIC 

UNITS  OF  TIME 


Measure  of  Time 

60  seconds  (sec.)  =  1  minute  (min.) 
60  minutes  =  1  hour  (hr.) 

24  hours  =  1  day  (da.) 

7  days  =  1  week  (wk.) 

12  months  (mo.)  =  1  year  (yr.) 

365  days  =  1  common  year 

366  days  =  1  leap  year 

MISCELLANEOUS  UNITS 

12  units    =  1  dozen  (doz.) 
20  units    =  1  score 
24  sheets  =  1  quire 
20  quires  =  1  ream 

1.  Commit  these  tables  to  memory. 

2.  A  man  ran  100  yd.  in  10  sec.     What  is  the 
unit  of  length  ?     Of  time  ?     Give  instances  in  which 
1  min.  is  the  unit  of  time.      1  hr.      1  da.      1  wk. 
1  mo.     1  yr. 

3.  Name  things  that  are  bought  and  sold  by  the 
quart,  liquid  measure ;  by  the  gallon ;  by  the  pint ; 
by  the  gill.     Of  what  use  is  the  gill  ? 


LESSON   80  181 

4.  Red  raspberries  are  sold  in  boxes  of  what  size  ? 
Why?     Strawberries  are  measured  by  units  of  what 
size  ?     Why  ? 

5.  Name  articles  that  are  sold  by  the  peck;  by 
the  bushel. 

6.  Why  is  the  quart  measure  generally  used  by 
milkmen  to  measure  their  milk  ?     Why  is  the  quart 
measure  not  a  convenient  measure  to  use  in  selling 
kerosene  ? 

7.  Why  is  pepper  put  up  in  £-lb.  or  J-lb.  bottles 
instead  of  in  larger  quantities  ? 

8.  Why  is  the  price  of  eggs  quoted  at  so  much  a 
dozen  instead  of  at  so  much  each  ?    Name  other  arti- 
cles, the  price  of  which  is  quoted  by  the  dozen. 

9.  Flour  is  sold  in  sacks  containing  -J-  bbl.  (24J  lb.), 
J  bbl.  (49  lb.),  and  by  the  barrel  (196  lb.).     Why 
are  these  convenient  quantities  ? 

10.  Butter  is  put  up  for  sale  in  1-lb.,  2-lb.  rolls  and 
in  5-lb.  pails.     Why  are  these  convenient  quantities  ? 

11.  Name  things  sold  by  the  ton ;  measured  by  the 
acre  ;  by  the  square  mile. 

12.  Why  are  spices  sold  by  the  ounce  ?     Give  in- 
stances in  which  one  dozen,  one  score,  one  quire,  and 
one  ream  are  used  as  units  of  measure. 

13.  How  might  such  expressions  as  the  following 
arise  by  acts  of  measurement :  2  yd.  1  ft.  6  in. ;  1  gal. 
2  qt.  1  pt. ;  8  bu.  2  pk. ;   2  lb.  8  oz. ;  4  T.  500  lb. ; 
6  yr.  4  mo. ;  2  hr.  20  min.? 


182  ARITHMETIC 

14.  How  might  such  statements  as  the  following 
arise  by  acts  of  measurement : 

24in.  =  12x2in.    24  in.  =  8x3  in.     24  in.  =  6x4    in. 
24in.=  4x6in.    24  in.  =  3  x  8  in.    24  in.  =  2x!2  in. 

What  is  the  ratio  of  24  in.  to  2  in.?     Of  24  in.  to 
3  in.  ?     To  4  in.  ?     To  6  in.  ?     To  8  in.  ?     To  12  in.  ? 

15.  In  question  14,  name  the  different  units  that 
have  been  used  to  measure  the  quantity,  24  in.     Name 
the  numbers. 

As  the  unit  becomes  larger,  what  change  takes 
place  in  the  number?     What  is  their  product? 

16.  What  two  things  are  necessary  to  express  the 
measurement  of  a  quantity?     How  can  you  obtain 
the  quantity  from  the  number  and  the  unit? 

17.  In  the  following  examples  what  are  the  quan- 
tities measured  by  the  given  numbers  and  units  ? 

Number  Unit  Number  Unit 

4  2  qt.  37  da. 

3  2  in.  63  doz. 

4  f  5  55  sq.  in. 
3  $10  8        10  A. 

18.  If  the  quantity  36  in.  is  measured  by  a  4-in. 
unit,  what  number  expresses  the  measurement  ? 

19.  In  the  following  examples  what  numbers  ex- 
press the  measurements? 


Quantity 

Unit 

Quantity 

24  hr. 

8hr. 

3bu. 

30^ 

6* 

6bu. 

2  da. 

6hr. 

48 

120 

$5 

4-in.  sq. 

$1 

1  dime 

1  qt. 

4  gal. 

2qt. 

1ft. 

LESSON  81  183 

Unit 

Ipk. 
4pk. 

1  doz. 

2  sq.  in. 
Igal. 
lyd. 

20.  If  the  number  8  expresses  the  measurement  of 
the  quantity  40  in.,  what  is  the  unit?     How  can  you 
obtain  the  unit  from  the  number  and  the  quantity? 

21.  In  the  following  examples  what   units   have 
been  used  to  measure  the  quantities? 

Quantity  Number  Quantity  Number 

112  6  $200  10 

30  da.  5  $200  20 

2  bu.  4  6  gal.  12 

15  doz.  5  35^  5 

22.  How  do   you   obtain   the    quantity   from   the 
number  and  unit?     The  unit  from  the  quantity  and 
number  ?     The  number  from  the  quantity  and  unit  ? 

Lesson  81 

1.  What  is  the  quantity  measured  by  the  number 
6  when  the  unit  is  3  gal.  2  qt.  of  milk  ? 

2.  Find  the  weight  of  the  unit  that  measures  the 
quantity  9  Ib.  8  oz.  4  times. 

3.  To  what  unit  must  2  yd.  1  ft.  6  in.  be  reduced 
in  order  to  find  the  number  of  times  it  is  measured 


184  ARITHMETIC 

by  the  unit  3  in.  ?  Find  this  number.  This  number 
is  often  called  the  ratio  of  2  yd.  1  ft.  6  in.  to  3  in. 
If  you  actually  measured  a  line  2  yd.  1  ft.  6  in.  long 
by  the  unit  3  in.  to  find  this  number,  would  it  be 
necessary  to  reduce  2  yd.  1  ft.  6  in.  to  inches  ? 

4.  Find  the  ratio  of  5  bu.  1  pk.  to  3  pk.  Find  the 
cost  of  5  bu.  1  pk.  of  potatoes  at  the  rate  of  3  pk. 
for 


5.  Make  a  drawing  to  represent  a  field  120  yd. 
long  and  80  yd.  wide.     How  long  must  a  wire  be  to 
go  around  it  ?    What  would  be  its  cost  at  6  ^  a  yard  ? 
What  would  4  rows  of  wire  fencing  cost? 

6.  What  would  4  rows  of  wire  fencing  cost  for  a 
chicken  coop  6  yd.  long  and  4  yd.  wide  at  6  ^  a  yd.? 

7.  If  a  yard  measure  is  ^  in.  too  long,  what  is  the 
actual  distance  between  two  points  which  are  found 
by  this  measure  to  be  6  yd.  apart? 

8.  A  200-acre  farm  is  sown  with  grain  as  follows  : 
barley  25  A.,  oats  46  A.,  wheat  75  A.     The  buildings, 
garden,  and  orchard   occupy  12  A.,  and  the  rest  is 
pasture.     How  many  acres  of  pasture  are  there  ? 

9.  A  map  is  drawn  so  that  half  an  inch  represents 
1  mi.    What  will  1  in.  represent?    How  many  square 
miles  will  1  sq.  in.  represent? 

10.   Find  the  weight  of  an  iron  bar  1  ft.  long  if 
1  yd.  weighs  18  Ib. 


LESSON  81  185 

Find  the  weight  of  an  iron  bar  4  yd.  2  ft.  long,  of 
which  1  yd.  weighs  15  Ib. 

11.  Find  the  cost  of  fencing  a  piece  of  railway 
(both  sides),  7  rd.  long,  at  $5.50  a  rod? 

12.  A  block  of  stone  is  8  in.  long,  6  in.  wide,  and 
4  in.  thick.     Find  its  weight  if  6  cu.  in.  weigh  1  Ib. 

13.  A  merchant  buys  28  yd.  of  cheese  cloth  at  6  $  a 
yd.     He  uses  a  certain  number  of  yards  in  his  store 
and  sells  the  remainder  for  the  total  cost  price  at  7  ^  a 
yard.     How  many  yards  does  he  sell?     How  many 
does  he  use  ? 

14.  What  does  a  bushel  of  wheat  weigh  ?     If  3  Ib. 
of  wheat  makes  2  Ib.  of  flour,  how  many  pounds  of 
flour  will  1  bu.  of  wheat  make  ? 

15.  Find  the  cost  of  cementing  the  floor  of  a  cellar 
6  yd.  long  and  5  yd.  wide  at  12^  per  sq.  yd. 

16.  Find  the  cost  of  digging  a  cellar  4  yd.  long, 
3  yd.  wide,  and  2  yd.  deep,  at  20^  per  cu.  yd. 

17.  A  certain  map  is  drawn  so  that  2  mi.  is  repre- 
sented by  1  in.     On  this  map  the  township  of  Scott 
is  a  square  whose  side  is  3  in.     What  is  the  length 
of  the  township  ?     What  is  its  area  ? 

18.  Find  the  number  of  strips  of  paper  in  the  wall 
of  a  room  24  ft.  long  and  20  ft.  wide,  the  paper  being 
2  ft.  wide.     What  is  the  unit  here  ? 


186 


ARITHMETIC 


19.  A  farmer  sowed  3  pk.  of  wheat  in  a  small  field 
and  raised  14  bu.  1  pk.  of  seed.    What  is  the  average 
yield  per  peck  of  seed  ? 

20.  An  express  train  takes  8  hr.  20  min.  to  travel 
320  mi.     If  stops  of  5  min.  each  are  made  at  4  dif- 
ferent places,  find  the  average  rate  at  which  the  train 
is  travelling. 

21.  A  railway  train  travels  at  the  rate  of  1  mi.  in 
2  min.     What  is  its  speed  per  hour? 


Lesson  82 


1.   What  is  the  sum  of : 
788 
989 


Add: 


8 
39 


48 


9 
59 


9 
10 


9 
30 


10 

8 


9 

28 


8 

7 

60 


9 

3 

45 


9 

9 

80 


6          7 

2          8 

98        90 


4 

3 

91 


4. 

4 

1 

2 

3 

4 

8 

7 

9 

2 

4 

8 

9 

8 

4 

5 

6 

9 

8 

5 

5 

5 

3 

2 

3 

19 

27 

22 

45 

63 

71 

83 

90 

LESSON  82  187 


Add: 
5.    $39.46 

86.74 

$45.49 
23.87 

$38.94 
59.36 

$97.56 
36.79 

$352.69           $ 
176.29 

388.14 
279.56 

$6243.80 
2597.80 

$1873.45 
2794.63 

6.    $165.95 

258.71 
147.58 

$229.69 
141.65 
299.57 

$370.80 
156.93 
881.79 

$179.79 
324.67 
250.60 

7.  A   merchant   sold   goods   on    Monday  to   the 
value  of  $187.91,  Tuesday  $254.82,  and  Wednesday 
$181.79.     What  were  the  total  sales  on  these  three 
days? 

8.  A  farmer  sold  23  bu.  wheat  for  $24.84,  34  bu. 
for  $33.31,  and  15  bu.  barley  for  $14.70.     How  many 
bushels  of  grain  did  he  sell  and  for  how  much  ? 

Subtract : 

9.  $37.33         $28.77         $427.97         $626.78 

29.38  19.89  368.48  349,79 

10.  $356.71     $3026.69       $2281.79       $6006.25 

248.24        1456.84          1584.82          3750.82 

11.  A  real  estate  agent  bought  a  lot  for  $1880  and 
sold  it  for  $  2375.     Find  his  gain. 

12.  A  man  paid  $137  for  one  horse  and  $89  for 
another.     They  cost  him  for  feed  $24.75.     He  sold 
them  for  $275.     Find  his  gain. 


188 


ARITHMETIC 


13.  Find  the  amount  of  the  following  bill : 

6  pairs  of  stockings  at  3  for  $  1.00. 
24  handkerchiefs  at  $1.75  per  doz. 
6  yd.  cloth  at  $.48  a  yd. 
3  yd.  muslin  at  $.15  a  yd. 

14.  A  farmer's  wife  sold  20  Ib.  of  butter  at  15  $  a 
pound.     She  then  bought  16  Ib.  of  sugar  at  5|^  a 
pound,  and  2  Ib.  of  tea  at  60  £  a  pound.     How  many 
pounds  of  raisins  at  8  ^  a  pound  can  she  buy  with  the 
rest  of  her  money  ? 

Lesson  83 

1.    Count  by  9's  from  9  to  108. 
Count  by  9's  from  108  to  9. 


2.   Memorize : 


Nine  times 


1  is     9 

5  is  45 

9  is     81 

2  is  18 

6  is  54 

10  is     90 

3  is  27 

7  is  63 

11  is     99 

4  is  36 

8  is  72 

12  is  108 

3.  In  the  table  of  9's  what  is  the  sum  of  the  two 
digits  in  each  product? 

4.  Name  the  numbers  less  than  100  of  which  9 
is  a  factor.     What  number  is  the  greatest  common 
factor  of  18  and  24 ;  18  and  45 ;  35  and  56 ;   63  and 
81;  40  and  55;  99  and  72? 


LESSON  83  180 

5.  What  is  the  largest  unit  that  will  divide  45  A. 
and  63  A.  ?     Two  farms  contain,  respectively,  45  A. 
and  63  A.     If  these  two  farms  are  divided  into  fields 
of  equal  size,  containing  as  many  acres  as  possible, 
how  many  acres  will  there  be  in  each  field?     How 
many  fields  ? 

Multiply: 

6.  1514.02      11180.66        $26.55          $97.22 
7      8        9          9 

7.  $851.02        $738.75      $243.44      $1097.47 
9        9      9      9 

8.  What  number  smaller  than   20  has   9  for  a 
factor?     Smaller  than  25?     61?      33?     70?     80? 
82?     74?     26?    44? 

9.  Give  the  quotient  and  remainder  on  dividing 
$231  by  9;  $868  by  $9;  798  mi.  by  9;  676  of  any 
unit  by  9  -,  319  of  any  unit  by  9  of  the  same  unit. 

10.  A  speculator  gave  his  check  for  the  price  of 
9  city  lots  at  $  2450  apiece,  and  after  this  was  cashed 
he  still  had  $1250  in  the  bank.     How  much  had  he 
at  first? 

11.  A  farmer  got  315  bu.  of  oats  off  a  nine-acre 
field.     How  many  bushels  to  the  acre  ? 

State  the  corresponding  question  in  which  you  are 
required  to  find  the  number.     The  quantity. 

12.  In  how  many  days  would  a  man  walk  216  mi., 
at  the  rate  of  3  mi.  an  hour  for  9  hr.  a  day  ? 


190  ARITHMETIC 


13.  What  is  the  ratio  of  3  dots  to  4  dots  ?  Of  4 
dots  to  3  dots  ?  If  each  dot  represents  6  ?,  what  will 
3  dots  represent  ?  4  dots  ?  What  is  the  ratio  of  1  8  4 
to  24??  Of  24?  to 


14.   If  24?  will  buy  a  peck  of  peas,  what  part  of  a 
peck  will  18?  buy?     How  many  quarts? 


15.  What  is  the  ratio  of  4  dots  to  6  dots?     If  each 
dot  represents  9  yd.,  what  will  4  dots  represent?     6 
dots  ?     What  is  the  ratio  of  36  yd.  to  54  yd.  ?     Of 
54  yd.  to  36  yd.  ? 

16.  If  54  yd.  of  cloth  cost  $  67.50,  what  will  36  yd. 
of  the  same  kind  cost? 

If  54  men  can  do  a  piece  of  work  in  6  da.,  how 
long  will  it  take  36  men  to  do  it? 

17.  Refer  to  the  dots  in  question  15  and  give  the 
value  of  1  dot,  2  dots,  3  dots,  4  dots,  5  dots,  and 
6  dots,  when  each  dot  represents  9  Ib. 

18.  What  is  the  ratio  of  9  Ib.  to  36  Ib.  ?     Of  36  Ib. 
to  9  Ib.?     Of  18  Ib.  to  45  Ib.?     Of  45  Ib.  to  18  Ib.? 
Of  27  Ib.  to  54  Ib.  ?    Of  54  Ib.  to  27  Ib.  ? 

19.  If  18  Ib.  of  coffee  cost  1  5.40,  what  will  45  Ib. 
cost  at  the  same  rate  ? 

20.  54  T.  of  coal  cost  $310.50.     What  will  27  T. 
cost  at  the  same  rate  ? 


LESSON  84 


191 


21.  What  is  the  ratio  of  4  5-cd.  of  wood  to  9  5-cd. 
of  wood  ?    Of  20  cd.  to  45  cd.  ?     Of  45  cd.  to  20  cd.  ? 
If  45 'cd.  of  wood  cost  $144,  what  will  20  cd.  cost? 

22.  If  36  T.  of   hay  cost  1 320,  what  will  27  T. 
cost? 

23.  The  value  of  a  purse  and  the  money  within  it 
is  $12.     If  the  ratio  of  the  money  to  the  value  of  the 
purse  is  3,  find  the  value  of  each. 


Lesson  84 

1.    Memorize  : 

Ten  times 

lislO 

5  is  50 

9  is    90 

2  is  20 

6  is  60 

10  is  100 

3  is  30 

7  is  70 

11  is  110 

4  is  40 

Sis  80 

12  is  120 

2.  In  what  figure  do  all  these  products  of  10  end  ? 

3.  Multiply: 

35        62        288        164        2164         3256 
10        10          10          10  10  10 

In  what  figure  do  all  these  products  of  10  end? 

4.  What  is  the  easiest  way  of  multiplying  a  num- 
ber by  10?      Write  the  product  of   these   numbers 
multiplied  by  10: 

•  16,    21,     24,    43,    72,     245,    631,    725. 


ARITHMETIC 


5.  Multiply  16  by  10  and  the  product  by  10.    How 
can  you  multiply  a  number  by  10  twice  in  succession 
without  actually  multiplying  ?     How  can  you  multi- 
ply a  number  by  100  without  actually  multiplying  ? 

6.  Write    the    product   of    these   numbers   when 
multiplied  by  100: 


5,     8,     12, 

24,     35,     68,     215,     625. 

1 

x 

11=11 

11 

x 

1=? 

8.1 

x  12  =  12 

12  x   1=? 

•2 

x 

11  =  22 

11 

x 

2=? 

2 

x  12  =  24 

12 

x 

2  =  ? 

3 

X 

11  =  33 

11 

X 

3=? 

3 

x!2  =  36 

12 

x 

3=? 

4 

X 

11  =  44 

11 

X 

4  =  ? 

4 

x!2  =  48 

12  x 

4=? 

5 

X 

11  =  55 

11 

X 

5=? 

5 

x  12  =  60 

12 

X 

5=? 

6 

x 

11  =  66 

11 

X 

6=? 

6 

x  12  =  72 

12 

x 

6=? 

7 

X 

11  =  77 

11 

X 

7=? 

7 

x  12  =  84 

12 

X 

7=? 

8 

X 

11  =  88 

11 

X 

8=? 

8 

x  12  =  96 

12 

X 

8=? 

9 

X 

11  =  99 

11 

X 

9  =  ? 

9x12  =  108 

12 

X 

9  =  ? 

10 

X 

11  =  110 

11 

X 

10  =  ? 

10 

x  12  =  120 

12 

X 

10  =  ? 

11 

X 

11=   ? 

11 

X 

11  =  ? 

11 

x  12=132 

12 

X 

11  =  ? 

12 

X 

11=   ? 

11 

X 

12=? 

12 

x  12=144 

12 

X 

12  =  ? 

9.    Write   out   and  memorize    the    multiplication 
tables  of  11  and  12. 

10.  What  is  the  area  of  a  square  whose  side  is 
12  in.  ?     How  many  square  inches  in  a  square  foot? 

11.  In  a  garden  there  are  12  rows  of  potatoes  with 
11  hills  in  a  row;   how  many  hills  of  potatoes  are 
there  in  the  garden?     Name  the  number,  unit,  and 
quantity.     State  the  corresponding  question  in  which 
you  are  required  to  find  the  number.     The  unit.. 


LESSON  84 


193 


12.  If  1  pk.  of  potatoes  is  obtained  from  each  hill 
on  the  average,  what  is  the  yield  in  bushels  ? 

13.  Review  the  Multiplication  Table : 


Two-  times 

Three  times 

Four  times 

Five  times 

Six  times 

Seven  times 

1  is    2 

lis   3 

1  is   4 

1  is    5 

1  is    6 

lis    7 

2  "    4 

2  "   6 

2  "    8 

2  "  10 

2  "  12 

2  "  14 

3  "    6 

3  "    9 

3  "  12 

3  "  15 

3  "  18 

3  "21 

4  "    8 

4  "  12 

4  "  16 

4  "20 

4  "24 

4  "28 

5  "  10 

5  "  15 

5  "  20 

5  "25 

5  "  30 

5  "35 

6  "  12 

6  "  18 

6  "24 

6  "  30 

6  "  36 

6  "42 

7  "  14 

7  "21 

7  "28 

7  "35 

7  "42 

7  "49 

8  "  16 

8  "24 

8  "32 

8  "40 

8  "48 

8  "56 

9  "  18 

9  "27 

9  "36 

9  "45 

9  "  54 

9  "63 

10  "  20 

10  "  30 

10  "  40 

10  "  50 

10  "  60 

10  "  70 

11  "  22 

11  "  33 

11  "  44 

11  "  55 

11  "  66 

11  "  77 

12  "  24 

12  "  36 

12  "  48 

12  "  60 

12  "  72 

12  "  84 

Eight  times 

Nine  times 

Ten  times 

Eleven  times 

Twelve  times 

lis    8 

lis     9 

1  is    10 

1  is    11 

lis    12 

2  "  16 

2  "    18 

2  "    20 

2  "    22 

2  "    24 

3  "  24 

3  "    27 

3  "    30 

3  "    33 

3  "    36 

4  "  32 

4  "    36 

4  "    40 

4  "    44 

4  "    48 

5  "40 

5  "    45 

5  "    50 

5  "    55 

6  "    60 

6  "48 

6  "    54 

6  "    60 

6  "    66 

6  "    72 

7  "  .56 

7"    63 

7  "    70 

7  "    77 

7  "    84 

8  "64 

8  "    72 

8  "    80 

8"    88 

8  "    96 

9  "  72 

9  "    81 

9  "    90 

9  "    99 

9  "  108 

10  "  80 

10  "    90 

10  "  100 

10  "110 

10  "  120 

11  "88 

11  «    99 

11  "  110 

11  "121 

11  "  132 

12  "  96 

12  "  108 

12  "  120 

12  "  132 

12  "  144 

SECTION  X 


Lesson  85 

Read  the  following  quantities  : 

1.  $1000       $2000       $6000       $8000      $625 
$1625       $4625       $6615       $8314      $9276 

2.  $12,000        $18,000        $46,000        $90,000 

$423  $12,423        $25,428        $36,250 

$58,736        $60,235        $60,035        $80,005 

3.  $438  $438,000  $649,000 
$625,346             $549,763             $245,084 
1333,333             $325,040             $520,006 

4.  $1,000,000          $4,000,000          $6,000,000 
$1,250,000          $4,645,000          $6,236,124 

$2,825,127          $2,478,042          $4,048,026 

5.  $312.83  $2678.28  $1052.47 
$45,624.25          $17,322.50          $30,420.08 
$70,055.04          $841,762.50        $123,750.65 

Write  in  figures  : 

6.  Six  hundred  twenty-five ;  eight  hundred  sixtj; 
five  hundred  seventy-six ;  one  thousand  two  hundred 
forty-six;  two  thousand  sixty;  three  thousand  eighty; 
six  thousand  eight ;  nine  thousand  nine. 

194 


LESSON  85  195 

7.  Fifteen    thousand    three    hundred    fifty-four ; 
seventy-five  thousand  two  hundred  forty-nine ;  ten 
thousand  two  hundred  fifty ;  twenty  thousand  four 
hundred  five  ;  sixty-four  thousand  twenty-six ;  eighty 
thousand  seven. 

8.  Three  hundred  twentj^-four  dollars  and  twenty- 
five  cents ;   two  thousand  six  hundred  fifty  dollars 
and  four  cents;    forty-five  thousand  nine  hundred 
ninety-eight   dollars   and   twenty-three  cents ;    two 
hundred  seventy-six  thousand  five  hundred  four  dol- 
lars and  seventeen  cents. 

9.  Review  these  addition  tables : 

12        123        123 
43       543       654 

1234  1234 

1  i  £  i        il65 

12345       2345 

98765       9876 

3456     456     567 

9_   8   7^   6     9   8_   7     987 

67      78      8      9       9 
98      98      9      9      10 


196  ARITHMETIC 


Add: 

10. 

1811.04 

1360.00 

1   26.55 

$851.02 

650.12 

215.17 

418.60 

312.60 

19.25 

12.50 

20.63 

147.22 

32.50 

311.20 

105.24 

568.35 

113.56 

235.32 

222.42 

116.02 

11. 

$  636.99 

$  859.69 

$     97.22 

$1180.66 

1850.14 

2223.42 

8148.60 

342.65 

311.20 

1097.47 

3839.25 

1237.50 

1201.64 

1214.03 

694.62 

2678.28 

12.  New  Hampshire  contains  9305  sq.  mi.,  Ver- 
mont 9565,  Massachusetts  8315,  Rhode  Island  1256, 
Connecticut  4990.     What  is  the  total  area  of  these 
five  states? 

13.  This   total   area   is   how  many   square   miles 
greater  than  that  of  Maine,  the  area  of  which  is 
33,040  sq.  mi.? 

Subtract : 

$403.59       $875.13     $6168.37       $1035.42 
94.63          694.73          467.89  559.83 

$3839.25     $5300.20     $7357.51     $36,501.28 
15<      3661.09        1214.03        1777.60       21,420.64 

16.  Vermont  contains  9565  sq.  mi.  and  Massachu- 
setts 8315  ;  what  is  the  difference  in  their  areas  ? 

17.  Lake   Erie   contains    7750    sq.    mi.,    Ontario 
6950,  and  Michigan  22,000.      How  much  larger  is 


14. 


LESSON   86  197 

Lake  Michigan  than  the  united  area  of  Lake  Erie 
and  Lake  Huron  ? 

18.  A,  B,  and  C  engaged  in  trade;  A  put  in 
82450,  B,  13275,  and  C  as  much  as  A  and  B  together. 
How  much  money  did  C  put  into  the  business  ? 
What  was  the  total  capital? 


Multiply  : 
19.      134.71 
8 

$28.79 
6 

$33.72 
9 

$24.95 
5 

20.   $134.36 
4 

1364.76 

7 

$1763.29 
8 

$2678.28 
9 

21.  A  is  worth  $3275,  and  B  4  times  as  much. 
What  is  B  worth  ? 

22.  Divide : 

6)15876.40     7)$  4956. 35     8)13008.96     9)15842.35 

23.  A  dealer  bought  sheep  at  the  average  rate  of 
$  6  each  ;  how  many  did  he  buy  for  $  3816  ?     What 
are  you  given  ?     What  are  you  required  to  find  ? 

24.  A  furniture  dealer  gains  $  1296  buying  sofas 
for  $18.75  each  and  selling  them  for  $27.75.     How 
many  did  he  sell  ?     What  is  the  unit  here  ? 

Lesson  86 

l.    64,395  is  equal  to  5  units,  9  tens,  3  hundreds, 
4  thousands,  6  ten-thousands. 


198  ARITHMETIC 

2.  Give,  as  in  question  1,  the  place  value  of  each 
figure:    25;  37;  -272;    582;   6548;    2094;   42,965; 
37,048. 

3.  What  is  the  units'  place,  the  tens'  place,  the 
hundreds',  the  thousands',  the  ten-thousands'  ? 

4.  Multiply  2  tens  by  3,  how  many  tens?     Mul- 
tiply 2  by  3  tens,  how  many  tens  ?     Multiply  4  tens 
by  5,  by  6,  by  7,  by  8 ;  how  many  tens  in  each  case  ? 
Multiply  4  by  5  tens,  by  6  tens,  by  7  tens,  by  8  tens  ? 
How  many  tens  in  each  case  ? 

5.  25  units  =  ?  units  tens. 

24  tens   =  ?  tens  hundreds. 
58  tens   =  ?  tens  hundreds. 
32  units  =  ?  units  tens. 
64  tens   =  ?  tens  hundreds. 
16  tens   =  ?  tens  hundreds. 

6.  3  tens  multiplied  by  2  equals  6  tens. 

3  tens  multiplied  by  2  tens  equals  6  what? 
6  tens  multiplied  by  4  tens  equals  what  ? 
6  tens  multiplied  by  2  tens  equals  what  ? 

7.  68     Multiply  68  by  4,  and  the  product  is  272. 
24   The  7  is  7  what?     The  2  in  24  is  2  what  ? 

272   Multiply  8  by  2  tens  and  the  product  is 
186     16  tens  or  1  hundred  6  tens.     Place  6  tens 
3       under  7  tens,  and  carry  the  1  to  the  hun- 
dreds' place.     Multiply  6  tens  by  2  tens,  and  the 
product  is  12  hundreds.     To  this  add  1  hundred, 


LESSON  86  199 

and  the  sum  is  13  hundreds.     Add,  and  the  complete 
product  is  1632. 

8.  Study  question  7,  then  place  24  under  68  and 
multiply  without  looking  at  the  book.     Do  this  until 
you  can  work  quickly  and  accurately. 

9.  Multiply  : 

38  58  36  76  $64  $47 

24  24  24  32  25  16 

10.  A  bushel  of  oats  weighs  32  Ib.  ;  how  many 
pounds  in  48  bu.? 

11.  A  page  of  a  book  contains  39  lines,  averaging 
13  words  to  a  line.     Find  the  number  of  words  on 
the  page. 

12.  A  speculator  buys  25  A.  of  land  at  $65  an 
acre  and  sells  it  for  $  88  an  acre.     Find  his  gain. 

13.  Multiply : 

00        (ft)        00  00         00          CO 

$35         $17         32  Ib.          27  mi.         19  mi.         $48 
_28         __13         68_  38  16  24 

14.  Question  13  shows   the   multiplications  that 
must  be   done   for   simple   practical   examples   like 
questions  10,  11,  12. 

Write  out  these  examples  : 

(a)  About  the  cost  of  28  cows  at  $35  each. 

(b)  About  the  gain  on  selling  13  horses. 

(c)  About  the  number  of  pounds  in  68  bu.  of  oats. 


42 

79 

89 

93 

75 

86 

39 

67 

99 

58 

94 

86 

231 

176 

224 

168 

365 

893 

24 

32 

13 

43 

64 

75 

200  ARITHMETIC 

(ct)  About  the  distance  a  boy  rides  on  his  bicycle 
in  38  days. 

(e)  About  the  distance  apart  two  boats  will  be, 
one  going  down  stream  at  11  mi.  an  hr.,  the  other 
up  stream  at  8  mi.  an  hr. 

(/)  About  a  man's  savings  in  2  yr. 

Multiply : 
15. 


16. 


17.  $22.13  $43.07  $29.04  $34.45  $54.39  $47.81 
24  27  16  82  18  29 

18.  $39.17  $94.26  $87.91   $60.86  $68.77  $74.93 
45  66  89  19  95  68 

19.  A  business  man  pays  in  wages  $96.75  each 
week ;   what  wages  does  he  pay  in  1  yr.   (1  yr.  = 
52  wk.)? 

20.  How  far  will  a  bicyclist  travel  in  36  da.,  if  he 
travels  8  hr.  a  day  at  the  rate  of  9  mi.  an  hour? 

Lesson  87 

l.    Divide  714  by  21.  21)714(34 
2  is  called  the  trial  divisor.  63 

2  is  contained  in  7  3  times.     Multiply          ~^ 
21  by  3.     The  product  is  63.     Place  63  84 

under  71,  subtract,  and  bring  down  4. 


LESSON   87  201 

2  is  contained  in  8  4  times.     Multiply  21  by  4,  and 
write  the  product  84  under  84. 

The  quotient  is  34.     How  would  you  prove  34  the 
correct  answer? 

2.  What  is  the  trial  divisor  when  the  divisor  is 
21?  31?  41?  51? 

Find  the  quotients  : 

903-5-21         992 -r- 31         2542 -*- 41         3162-^-51 
11344-^-21  $1488-5- $31 

3.  What  is  the  trial  divisor  when  the  divisor  is 
22?    42?     62?     72? 

Find  the  quotients  : 

726 -i- 22        2352 -v- 42        4650 -f- 62         5188 -r- 72 
$726-^-22  =  ?      $2352-s-|42  =  ?      $4650  H-  62  =  ? 

4.  A  cattle  dealer  paid  $682  for  22  head  of  cat- 
tle.    What  was  the  average  price?     Name  the  quan- 
tity, number,  and  unit. 

5.  If  a  train  travels  32  mi.  an  hour,  how  long 
will  it  take  to  travel  1152  mi.,  there  being  stops 
amounting  to  one  hour? 

6.  How  many  cows  at  $  31  apiece  can  a  man  buy 
with  the  money  he  receives  for  9  horses  sold  at  an 
average  price  of  $  124  ? 

7.  What  is  the  cost  of   1472  Ib.  of   oats  at  9} 
a  bu.  ?     (1  bu.  oats  weighs  32  Ib.) 

8.  What  is  the  trial  divisor  when  the  divisor  is 
23,24,33,44,54,63,84? 


202  ARITHMETIC 

Divisor  Dividend  Quotient  Divisor  Dividend  Quotient 

9.    (a)  23)6285(273  (6)  24)3877(161 

46  24 

168  147 

161  144 

~T5  ~37 

69  24 

6  Remainder  13  Remainder 

(a)  The  trial  divisor  2  is  contained  in  the  trial 
dividend  6  3  times.  On  multiplying  23  by  3,  the 
product  69  is  seen  to  be  too  large.  Why  ?  Try  2 
in  the  quotient.  Again,  2  is  contained  in  16  8  times. 
On  multiplying  23  by  8,  the  product  184  is  seen  to 
be  too  large.  Why?  Try  7  in  the  quotient.  2  is 
contained  in  7  3  times.  The  remainder  is  6. 

(6)  On  the  second  division  2  is  contained  in  14  7 
times.  Why  is  7  too  large? 

(<?)  When  23,  24;  33,  34;  43,  44  ;  and  so  on,  are 
the  divisors,  the  quotient  obtained  by  using  the  trial 
divisor  is  frequently  too  large.  If  so,  try  in  the 
quotient  the  number  next  smaller. 

10.  Study   question   9   carefully,   then   copy   the 
examples,  and  divide.     Do  this  until  you  can  divide 
accurately  and  quickly  without  looking  at  the  book. 

11.  Find  the  quotients : 

•3197 -v- 23       5940 --44       5355 -r  68       12,936  +  84 


LESSON   88  203 

12.  Find  the  quotients  and  remainders : 

1527 -v- 34       2632 -f- 54       46,798-^64       2954-5-14 
7549  -=- 13     u  6493  -5-  84       26,495  +•  94       3823  -r-  44 

13.  How    many    days    are    there    in    1728    hr.  ? 
4008  hr.?     21,768  hr.? 

14.  How  many  sheets  of  paper  in  1  quire  ?     If  a 
business  man  uses  7488  sheets  of  paper  in  a  year, 
how  many  quires  does  he  use? 

15.  A  man  whose  salary  is  $40  a  week  spends 
$  26  a  week.    In  how  many  weeks  can  he  save  $686  ? 
What  is  the  unit  that  measures  his  savings  ? 

16.  A  speculator  paid  $6654  for  64  horses  and  85 
sheep.     If  the  sheep  cost  $6  apiece,  what  was  the 
average  cost  of  each  horse  ? 

Lesson  88 

Divisor  Dividend  Quotient         Divisor  Dividend  Quotient 

1.  (a)  29)7948(274   (6)  57)8898(156 
58  57 


214            118 
203              87 

319 

285 

118            31 
116 

2  Remainder 

348 
342 

Remainder 


(a)  As  29  is  nearly  equal  to  30,  the  trial  divisor  is 
3.     3  is  contained  in  7,  2  times,  in  21,  7  times,  and  in 


204  ARITHMETIC 

11,  3  times.  On  multiplying  29  by  3  the  product  is 
87.  On  placing  87  under  118  and  subtracting,  the 
remainder  is  31.  This  is  larger  than  29,  and  therefore 
the  quotient  is  1  larger  than  3,  or  4. 

(£)  On  the  last  division  the  trial  divisor  6  is  con- 
tained in  34  5  times.  Why  is  5  too  small? 

0)  When  27,  28,  29  are  the  divisors,  the  trial 
divisor  is  3.  What  is  the  trial  divisor  when  the 
divisors  are  37,  38,  or  39?  47,  48,  or  49?  57,  58,  or 
59?  67?  88?  99? 

2.  Name  the  trial  divisors.  Find  the  quotients 
and  remainders : 


5842  -  29 
9546  -4-  59 
8113-*-  67 

8572  -r-  98 

9843  -j-  25 
4554  ^  36 
3580  -  64 
3679  -v-  47 

3134  +  44 
8967  ^  79 
17,988  -j-  34 
97,445  -*-  67 

Prove  your  answers  correct  by  multiplying  and 
adding  in  the  remainder.  If  correct,  this  sum  will 
equal  the  dividend. 

3.  How  many  pounds  of  sugar  are  there  in  3600  oz.? 
(1  Ib.  =  ?  oz.)     What  would  it  cost  at  5^  a  Ib.  ? 

4.  A  farmer  sells  2160  Ib.  of  wheat  at  80 1  a  bushel. 
Find  the  number  of  bushels  and  the  total  selling  price. 
(1  bu.  of  wheat  weighs  60  Ib.) 

5.  Find  the  value  of  12,288  Ib.  barley  at  $.50  a  bu. 
(1  bu.  barley  weighs  48  Ib.) 


LESSON  68  205 

6.  A  farm  of  85  A.  cost  $6375  ;  what  is  the  price 
per  acre  ?     If  the  owner  of  this  farm  wishes  to  increase 
it  to  100  A.,  how  many  acres  must  he  buy,  and  what 
will  they  cost  at  the  same  rate  ? 

7.  If  25  wagons  cost  $1375,  what  will  1  cost? 
What  will  45  cost  at  $  3  apiece  less  ? 

8.  A  bicycle  dealer  bought  3  doz.  bicycles  for 
$1620;  how  many  could  he  have  bought  for  $2160? 

9.  Find  the  quotients  and  remainders : 
23,487  +-  31        58,049  -r-  28        44,555  -+•  63 
84,287  -f-  59         13,947  •*- 16         65,287  -f- 17 
86,777  -5-  92         30,049  ^  19         99,498  -5-  43 
38,695  -5-  67         78,243  H-  99        84,827  -5-  15 

10.  A  wholesale  merchant  paid  $13,625  to  a  manu- 
facturer for  rugs  at  $25  apiece.  How  many  did  he 
buy? 

Divide : 

5)$  37.50        6)$17.64        8)$  2.64 

4)$. 24  7)$. 98  2)$. 08 

12.    Find  the  quotients  : 


U3-31  $22.68-i-42  $743.50-25 

$64.68-^22  $84.42-5-63  $369.84-67 

$42.68-=-22          $13.50-5-18  $854.37-5-99 

13.  If  25  T.  of  coal  cost  $121.25,  find  the  price 
per  ton. 

14.  If  a  dozen  and  a  half  boxes  of  soap  cost  $56.70, 
what  is  the  price  of  one  box  ? 


206  ARITHMETIC 

Lesson  89 

1.  Divide  $.72  by  $.06. 

1.06)1.72          Change  $.06  to  6^  and  $.72 
6  ,  72  j        to  72^  and  divide  6^  into  72^. 

12 

2.  Divide  $36.25  by  $.25. 

$.25)$36.25(  Change  $.25  to  25^ 

25^)3625^(145  and  $86;25  to  3625^ 

25  and    divide    25^    into 


100 
125 
125 

$l.SO-j-$.30=?   $3.25-*- 25^=?   $3.60-*- $.90=? 

4.  At  $.06  a  quart,  how  many  quarts  of  milk  can 
you  buy  for  $  .48  ?     How  many  gallons  ? 

5.  At  7  ^  a  cake,  how  many  cakes  of  soap  can  you 
buy  for  $.63  ?     How  many  boxes,  there  being  3  in  a 
box? 

6.  At  $.30  a  dozen,  how  many  dozen  lemons  will 
cost  $1.80? 

7.  How  many  pecks  of  potatoes  can  you  buy  for 
$.45  at  15^  a  peck?     What  part  of  a  bushel  ? 

8.  At  $.24  a  lb.,  how  many  pounds  of  butter  will 
cost  $1.92? 


LESSON  89  207 

9.    At  8^  a  lb.,  how  many  2-lb.  boxes  of  biscuits 

can  you  buy  for  $ .  64  ? 

10.  At  $.10  a  gal.,  how  many  5-gal.  cans  of  oil 
can  you  have  filled  for  $1.50? 

11.  A  lady  pays  $.96  for  dimity  at  $.12  a  yard. 
How  many  dresses    can  she  make  from  it  for  her 
little  girl,  if  each  dress  takes  4  yd.  ? 

12.  How  many  collars  can  you  buy  for  $2.00  at 
the  rate  of  3  for  50^? 

13.  A  merchant  bought  cloth  at  $.36  a  yard  and 
sold  it  for  $.45  a  yard.     His  gain  was  $22.50  ;  how 
many  yards  did  he  sell? 

14.  $8.32-1.16=  ?  $  9.45-i-$.35  =  ? 

$2.52-1.18=  ?  $15.84-$. 44=  ? 

$3.60-j-$.24=  ?  $14.25-f-$. 57=  ? 

15.  At  $  .35  a  basket,  how  many  baskets  of  peaches 
can  you  buy  for  $  25.20  ?     How  many  dozen  baskets  ? 

16.  At  28^  each,  how  many  hammers  can  you  buy 
for  $4.48? 

17.  How   many  bushels   of   potatoes,   at  $.65  a 
bushel,  can  you  buy  for  $11.05? 

18.  At  $.54  a  bushel,  how  many  bushels  of  corn 
can  you  buy  for  $176.04?     If  you  sell  the  corn  at 
58^  a  bushel,  what  is  your  gain? 

19.  A  grocer  bought  potatoes  in  the  fall  at  $.45 
a  bu.,  and  sold  them  in  the  spring  for  $.68  a  bu. 


208  ARITHMETIC 

His  gain  was  157.50;  how  many  bushels  did  he  buy  ? 
What  is  the  unit  that  measures  his  gain  ? 

20.  Bought  apples  at  55^  a  bu.  and  sold  them  at 
20  ^  a  pk.  If  my  gain  was  $  37.50,  how  many  bushels 
did  I  buy  ? 

Lesson  90 

1.  Write  in  figures  :    Two  hundred  twenty-five 
dollars  and  seventy-five  cents  ;  one  thousand  forty  dol- 
lars and  six  cents ;  six  thousand  three  hundred  dol- 
lars sixty-seven  cents. 

2.  Reduce  to  dollars  and  cents:   341^;   2159^; 
7804**;  25425^;  25039^. 

3.  Reduce  to  cents  :  $4;  16.25;  127.03;  $30.14; 
150.20;  $254.27;  $360.02. 

4.  A  farmer  receives  $29.25  for  wheat,  $19.02 
for  corn,  $7.25  for  vegetables,  and  $8.46  for  turkeys. 
What  does  he  receive  in  all  ? 

5.  A  lady  bought  a  bookcase  for  $9.98,  a  chair 
for  $5.35,  a  hat-rack  for  $11.50,  and  a  lounge  for 
$12.88.     Find  the  amount  of  her  bill. 

6.  Find  the  amount  of  these  bills  :  meat  $12.63, 
daily   paper    65^,  laundry   $2.36,   gas    $3.25,    and 
plumber  $1.70. 

7.  Ice  cream  salt  is  sold  at  ll  a  Ib.,  or  for  85^ 
per  100  Ib.   sack.     Find  what  is  saved  by  buying 
100  Ib.  at  a  time. 


LESSON  90  209 

8.  A  man  had  $5000  in  the  bank.     He  withdrew 
$3496.75;  how  much  remained  in  the  bank? 

9.  I   bought  a  horse  for   $150   and  a  cow  for 
$32.75,  and  paid  cash  $126.49.     How  much  is  still 
due? 

10.  A  lady  paid  64^  for  cotton,  75^  for  ribbon, 
$4.25  for  a  pair  of  shoes,  and  $3.73  for  cloth.    What 
change  should  she  have  left  from  a  ten-dollar  bill? 

11.  Find  the  amount  of  this  bill : 

3  cans  peaches  at  32^  each 

2  packages  gelatine  at  17^  each 
57  Ib.  sugar  at  19  Ib.  for  $1 

3  packages  cracked  wheat  at  11  $  each. 

12.  Find  the  amount  of  this  bill : 

2  Ib.  cheese  at  $.16  alb. 
51b.  butter  at  $.22  alb. 
10  Ib.  ham  at  12±^  alb. 
2  bottles  pickles  at  29  ^  each 
J  doz.  glasses  jelly  at  $4.40  a  doz. 

13.  If  25  Ib.  coffee  cost  $8.25,  what  is  the  cost 
of  1  Ib.  ? 

14.  A  merchant  received  $86.70  for  cloth  sold  at 
$.34  a  yard.     How  many  yards  were  sold? 

15.  Paid   $317.52   for  wheat   at   $.98  a  bushel. 
Find  the  number  of  bushels  bought. 

16.  A  merchant  bought  cloth  at  36^  a  yard,  and 
sold  it  for  $56.25  at  a  profit  of  9^  a  yard.     How 
many  yards  did  he  buy? 


SECTION  XI 


Lesson  91 

1.  In    the    expression   $2.34   the   3   is   3   what? 
What  part  of  a  dollar?     The  4  is  4  what?     What 
part  of  a  dollar?     The  34  is  34  what?     What  part 
of  a  dollar  ? 

2.  In  the  expression  $4.73  what  part  of  a  dollar 
is  the  7?     The  3?     The  73? 

3.  Read  as  dollars  and  hundredths   of  a  dollar: 

$2.31,  $4.65,  $7.60,  $6.05,  $6.46,  $6.09,  $.35,  $.06, 
$.43,  $.09. 

4.  Measure  with   a   metric   stick   and   count   the 
number  of  meters  (m.)  in  the  length  of  the  room. 
In  the  width. 

5.  Measure    different    lengths    with    the    metric 
stick. 

6.  Guess   at  two   points   on  the   blackboard   one 
meter  apart.     Test  by  measuring  with  a  metric  stick. 

7.  Count   the   number  of   decimeters  (dm.)  in  a 
meter.     How  many  ? 

210 


LESSON  91  211 

8.  One  decimeter  is  what  part  of   a  meter?     2 
decimeters  is  what  part  of  a  meter  ?     3  dm.  ?    6  dm.  ? 

9.  Measure  the  width  of  the  door  and  state  its 
width  in  decimeters. 

10.  Similarly  measure  the  width  of  your  desk  ;  its 
length ;  the  height  of  the  blackboard  above  the  floor, 
etc. 

11.  Cut  a   strip  of   cardboard  1  decimeter  long. 
Use  it  to  measure  the  metric  stick.     How  many  deci- 
meters in  a  meter  ? 

12.  1    meter   1   decimeter  is  written   1.1  meters, 
meaning  by  that  one  meter  and  one-tenth  of  a  meter. 
1  meter  2  decimeters  is  written  1.2  meters,  meaning 
one  meter  and  two-tenths  of  a  meter. 

1  m.  1  dm.  =  1.1  m.         1  m.  2  dm.  =  1.2  m. 
The  dot  between  the  1  and  1,  and  between  the  1  and 
2,  is  called  the  decimal  point.     It  separates  units  from 
tenths. 

13.  2.5   m.   is   read  two   and   five-tenths    meters. 
Read  similarly : 

1.3  m.,  2.4  m.,  3.6  m.,  4.2  m.,  6.8  m.,  .8  m.,  .2  m., 
.1  m. 

14.  Measure  the  length  of  the  room  and  express 
your  result  in  meters.     (Thus,  8.4  m.) 

15.  Measure  and  express   the  results  in  meters : 
The  width  of  the  room ;  points  taken  at  random  on 
the  blackboard  ;  the  heights  of  different  pupils,  etc. 


212  ARITHMETIC 

16.  Draw  an   oblong  .2  m.  long  and  .1  m.  wide. 
Take  points  1.4  m.  apart;  3.4  m.  apart;  4.6  m.  apart. 

17.  2.5   Ib.   is   read  two  and   five-tenths   pounds. 
Read  similarly :  2.5  da.,  2.7  hr.,  1.6  mi.,  4.8  yd.,  .8  yd., 
8.4  gal.,  .6  qt. 

18.  Write   in  figures,  using  contractions:    Three 
and  four-tenths  meters,  five  and  six-tenths  pounds, 
four  and  seven-tenths  dollars,  two-tenths  of  a  mile. 

19.  Count  the  number  of  centimeters  (cm.)  in  a 
decimeter ;  of  centimeters  in  a  meter. 

20.  Find  the  number  of  centimeters  in  the  height 
of  this  book ;  in  the  width. 

21.  Measure   the   number  of   centimeters   in   the 
length  of  a  line  of  this  book;   in  the  length  and 
width  of  a  sheet  of  paper,  length  of  a  lead  pencil, 
and  of  other  things. 

22.  Draw  an  oblong  12  cm.  long  and  8  cm.  wide. 

23.  ?  cm.  =  1  dm.     ?  dm.  =  1   m.     ?  cm.  =  1  m. 

1  cm.  is  what  part  of  1  dm.  ?     1  dm.  is  what  part  of 
1m.?     1  cm.  is  what  part  of  1  m.  ? 

24.  What  part  of  1  m.  is  2  cm.?    4  cm.?     8  cm.? 
15cm.?     25cm.?     36cm.? 

25.  1  dm.  2  cm.  =  ?  cm.     What  part  of  a  meter? 

2  dm.  4  cm.  =  ?  cm.     What  part  of  a  meter? 

26.  1  m.  1  dm.  1  cm.  is  written  1.11  m.,  meaning 
by  that  one  meter,  one-tenth  of  a   meter,  one-hun- 


LESSON  92  213 

dredth   of  a  meter,  or  one   and   eleven-hundredths 
meters. 

27.  4.68  m.  is  read  four  and  sixty-eight  hundredths 
meters.     Read  similarly : 

2.56  m.,  4.29  m.,  3.64  m.,  .45  m.,  .06  m.,  3.0T  m., 
5.60  m. 

28.  4.65  Ib.  is  read  four  and  sixty-five  hundredths 
pounds.     Read  similarly : 

2.25  Ib.,  3.17  mi.,  6.43  A.,  5.89  yr.,  .23  da.,  .64  hr., 
.04  hr.,  .06  gal.,  2.09  gal.,  4.06  bu.,  4.60  bu.,  3.49,  .75, 
2.09,  .06. 

29.  Take  two  points  4.62  m.  apart;  3.12  m.  apart ; 
2.40  m. ;  3.07  m. 

30.  In  the  expression  4.62  m.  the  place  value  of 
each  figure  is  given  thus :  4  is  four  meters,  6  is  six- 
tenths  of  a  meter,  and  2  is  two-hundredths  of  a  meter. 

Give  the  place  value  of  each  figure  in  the  follow- 
ing: 2.31  m.,  4.59  m.,  7.35  m.,  2.09  m.,  4.30  m.,  2.07  m. 

31.  Give  the  place  value  of  each  figure  in  the  fol- 
lowing: 2.15  Ib.,  3.74  mi.,  3.66  A.,  2.09  yr.,  .32  da., 
.64  hr.,  .06  yr.,  2.60  gal.,  4.65,  7.23,  .41,  2.04,  .04. 

Lesson  92 

1.  Count  the  number  of  millimeters  (mm.)  in  a 
centimeter ;  of  centimeters  in  a  decimeter ;  of  deci- 
meters in  a  meter ;  of  millimeters  in  a  meter. 


214  ARITHMETIC 

2.  Find  the  number  of  millimeters  in  the  width 
of  the  margins  of  this  book ;  in  the  thickness  of  this 
book  ;  in  the  length  of  the  printed  word  millimeter; 
in  the  distance  between  the  lines  on  ruled  paper ;  and 
in  other  short  distances. 

3.  Draw  and  cut  a  slit  2  mm.  wide  and  3  cm.  lonq- 

O 

in  a  sheet  of  paper. 

4.  ?  mm.  =  1  cm.     ?  cm.  =  1  dm.     ?  dm  =  1  m. 
?  mm.  =  1  m.     1  mm.  is  what  part  of  1  cm.  ?     1  cm. 
is  what  part  of  1  dm.  ?     1  dm.  is  what  part  of  1  m.  ? 
1  mm.  is  what  part  of  1  m.  ? 

5.  What  part  of  1  m.  is  2  mm.  ?   8  mm.  ?  25  mm.  ? 
84  mm.  ?     264  mm.  ?     625  mm.  ? 

6.  1  dm.  2  cm.  5  mm.  =  ?  mm.     What  part  of  a 
meter?     3  dm.  4  cm.  6  mm.  =  ?  mm.     What  part  of 
a  meter  ? 

7.  1  m.  1  dm.  1  cm.  1  mm.  is  written  1.111  m., 
meaning  one  meter,  one-tenth  of  a  meter,  one-hun- 
dredth of  a  meter,  one-thousandth  of  a  meter,  or  one 
and  one  hundred  eleven  thousandths  meters. 

8.  4.685  m.  is  read  four  and  six  hundred  eighty- 
five  thousandths  meters.     Read  similarly  : 

2.346  m.,  6.275  m.,  3.204  m.,  4.250  m.,  4.016  m., 
4.006  m.,  7.005  m.,  .214  m.,  .015  m.,  .006  m.,  .004  m., 
3.146  m. 

9.  4.625  Ib.  is  read  four  and  six  hundred  twenty- 
five  thousandths  pounds.     Read  similarly  : 


LESSON  92  215 

2.245  lb.,  2.145  T.,  T.543  A.,  5.019  A.,  7.016  yr., 
2.005  da.,  .243  da.,  .075  hr.,  .009  bu.,  .004  gal., 
3.468  mi.,  4.248,  .329,  .024,  .082,  .002,  .005. 

10.  Write  in  figures,  using  contractions  : 

One  and  three  hundred  sixty-eight  thousandths 
pounds  ;  nine  and  six  hundred  four  thousandths 
tons;  three  hundred  thirty -five  thousandths  of  a 
mile ;  forty-nine  thousandths  of  a  day ;  six  thou- 
sandths of  a  year ;  seventeen  thousandths  of  a  year. 

11.  Take  two  points  1.245  m.   apart;    2.436  m. 
apart;  3.104  m.;  2.005m. 

12.  What   is  the   place  value   of   each  figure  in 
question  11  ? 

13.  Give   the  place  value  of  each  figure  in  the 
following : 

3.764  m.,  8.157  lb.,  2.829  T.,  4.666  mi.,  8.095  A., 
1.906  A.,  3.008  yr.,  .247  yr.,  .016  yr.,  .009  mi., 
3.980  mi.,  5.823,  7.048,  .042,  .248,  .009. 

14.  Read  the  following  : 

2.15  2.356  80.004  666.016 

9.08  32.356  311.25  850.14 

73.25  432.356  636.09  189.1 

,      96.03  80.4  357.512  914.019 

245.2  80.04  201.001          10.011 

15.  What   is   the   place  value  of   each  figure  in 
the  last  column  of  question  14? 


216  ARITHMETIC 

16.  Show  on  a  metric  stick  the  following,  and 
note  carefully,  by  comparing  the  part  cut  off  with 
the  meter,  what  part  of  a  meter  each  quantity  seems 
to  be  : 

.25  m.,  .15  m.,  .356  m.,  .4  m.,  .246  m.,  .14  m. 

Lesson  93 


Copy  and  add  : 

1. 

2345 

234 

.5 

23. 

45 

2.345 

3482 

348 

.2 

34. 

82 

3.482 

6134 

613 

.4 

61. 

34 

6.134 

8753 

875 

.3 

87. 

53 

8.753 

2. 

64.215 

16. 

43 

222 

.342 

28.528 

24. 

213 

530 

.030 

21.835 

5. 

342 

112 

.458 

17.652 

44. 

653 

738 

.754 

3.  Write  in  columns  and  add  : 
2.174  +  5.073  +  4.256  +  3.543. 

.214  bu.  +  .876  bu.  +  .371  bu.  +  .444  bu. 

4.  Show  on   a  metric   stick  .214  m.,  .876   m., 
.371  m.,  .444  m. 

5.  Find  the  number  of  acres  in  a  farm  that  is 
divided   into    four   fields,    containing,   respectively, 
23.875  A.,  15.18  A.,  12.316  A.,  and  16.245  A. 

6.  In  the  following  question  draw  the  road  and 
mark  the  distances ; 


LESSON  93  217 

Four  towns,  A,  B,  C,  D,  lie  on  a  road  running 
north  and  south.  The  distance  from  A  to  B  is 
4.186  mi.,  from  B  to  C  6.56  mi.,  and  from  C  to  D 
8.514  mi.  Find  the  distance  from  A  to  D. 

Copy  and  subtract : 

7.  3.426 
1.312 

8.  3.42 


6.539 

38.492 

62.073 

2.153 

25.861 

44.444 

8.4 

6. 

796.873 

3.156 

4.251 

636.134 

1.204 

9.    From  a  piece  of  cloth  containing  16.5  yd.  I  cut 
12.375  yd.     How  much  was  left  in  the  piece  ? 

10.  From  a  farm  containing  100  A.  the  owner  sold 
32.875  A.     How  much  did  he  still  own  ? 

11.  A  man  bought  a  house  and  lot  with  .125  of 
his  money  and  invested  the  remainder  in  business. 
What  part  of  his  money  went  into  business  ? 

12.  Draw  a  line  and  mark  off  on  it  7  parts,  each 
.5  ft.  long.     Measure  the  whole  part  cut  off.     What 
is  its  length  ?     7  x  .5  ft.  =  ?  ft. 

13.  Add: 


.2yd. 

.3bu. 

.32  gal. 

2.64  A. 

.428  da. 

.2   « 

.3  « 

.32    " 

2.64  " 

.428  " 

.2   " 

.3  « 

.32    " 

2.64  « 

.428  " 

.2   « 

.3  " 

.32    « 

2.64  " 

.428  " 

218  ARITHMETIC 

Copy  and  multiply: 

14.  .2  yd.      .3  bu.     .32  gal.      2.64  A.      .428  da. 
_4  _4  _4  _J  _jt 

How  many  figures  are  there  to  the  right  of  the 
decimal  point  in  the  multiplicands  ?  In  the  products  ? 

15.  .141          1.98         3.452         8.234         26.019 

__6  _3         7         8         7 

As  you   multiply   give   the   place   value   of   each 
partial  product. 

16. 


17. 


18.  Look  at  the  metric  stick  and   find  out   the 
number  of  inches  in  one  meter.     If  1  meter  is  equal 
to  39.371  in.,  how  many  inches  long  is  a  line  that 
measures  3  meters  ? 

19.  Measure  a  line  3  meters  long  on  the  black- 
board, find  the  number  of  inches  in  it  by  measuring, 
and  test  the  correctness  of  the  answer  to  question  18. 

20.  What  will  25  loads  of  wheat  weigh,  the  aver- 
age weight  being  1.135  T.  ? 

21.  A  merchant  sold  45  yd.  of  cloth  a  day  at  a 
gain  of  $  .125  a  yd.    Find  his  gain  on  a  week's  sales. 


2.13 

4.25 

87.1 

.642 

.057 

16 

24 

36 

44 

64 

1.75 

99 

2.034 

27 

3.506 

81 

23.5 
69 

3.006 

72 

LESSON  94  219 

22.  Find  the  cost  of  48  thousand  feet  of  lumber 
at  $43.875  per  thousand. 

23.  Multiply  .36  by  24 ;    24  by  .36  ;    .256  by  6  ; 
6  by  .256  ;  8  by  .53.     Find  .53  of  1 8  ;  .64  of  96  yd.; 
2.54  of  26  ;  .26  of  254  ;  3.18  of  42  ;   .42  of  350  sheep. 

24.  A  drover  sold  .24  of  his  flock  of  250  sheep. 
How  many  did  he  sell  ? 

25.  Monday  a  merchant  sold  .924  of   a  piece  of 
cloth  containing  36  yd.     How  many  did  he  sell  ?     If 
the  rest  went  to   the   remnant   counter,  how  many 
yards  went  to  the  remnant  counter  ? 

Lesson  94 

1.  Divide  34.458  by  6. 

6  is  contained  in  34  5  times, 
6)34.458  in  44  tenths  7  tenths,  in  25  hun- 

5.743  dredths  4  hundredths,  and  in 

18  thousandths  3  thousandths. 

2.  Find  the  value  of  : 


8.  652  -=-4 

23.191  -=-  7 

8.992-5-4 

17.664-6 

4.996  +  2 

8.253  +  9 

84.708  +  9 

6.336-5-8 

4.995  +  5 

.897  +  3 

2.457  -r-  7 

25.938  +  3 

98.475  +  5 

.544  -r-  8 

86.824-8 

3.    If  a  vessel  travels  64,688  mi.  in  4  hr.,  what  is 
the  rate  per  hr.? 


220  ARITHMETIC 

4.  I  paid  $4.375  for  5  yd.  of  cloth.    What  was 
the  price  per  yd.? 

5.  If  1  bu.  contains  2150.42  cu.  in.,  how  many 
cubic  inches  will  1  qt.  dry  measure  hold  ? 

6.  If   1  gal.  holds  231  cu.  in.,  how  many  cubic 
inches  will  1  qt.  liquid  measure  hold? 

7.  Divide  357.84  by  42. 

42)357.84(8.52 

336  42  is  contained  in  357  8 

218  times,  in  218  tenths  5  tenths, 

210  in    84    hundredths    2    hun- 

84  dredths. 
84 

8.  Find  the  value  of : 

35.289^27  120.93-1-29 

106.08-^34  66.317 -r- 47 

3.266-^-23  2629.8  --54 

6.544  -=- 16  124.5  -*-  75 

As  you  divide  give  the  place  value  of  each  figure 
in  the  quotient. 

9.  I  paid  $ 2031.75  for  63  A.  of  farm  land.    Find 
the  cost  per  acre. 

10.  A  merchant  paid  $65.625  for  a  chest  of  tea 
containing  75  Ibs.  Find  the  cost  per  pound.  What 
would  be  the  total  gain  on  selling  it  at  $1  a  lb.? 


LESSON  94 


221 


11.  Divide  2.574  by  .6. 

Place  the  decimal  point  one 
place  to  the  right  in  both  di- 
visor and  dividend  and  divide 
as  in  the  example.  Why  can 
you  do  this  ? 

12.  Copy  and  divide  : 
,3)3.45  .4Y196 


.4)3.508 
.8)289.2 
.5). 3625 


.4)24  .6)15  .8)960  .9)10.8 

Give  the  place  value  of  each  figure  in  the  quotient. 

13.  Find  the  number  of  steps  in  a  stairs  between 
two  floors,  one  of  which  is  14.5  ft.  higher  than  the 
other,  if  each  step  is  .5  ft.  high.     Name  the  unit  of 
measure  and  the  quantity.     How  do  you  find  the 
number  when  the  unit  and  quantity  are  known  ? 

14.  A  drover  sold  .6  of  his  flock  of  sheep  and  had 
240  left.     Find  the  number  of  sheep  in  the  flock  at 
first. 

15.  A  merchant  sold  cloth  so  as  to  gain  .3  of  the 
cost.     If  the  gain  on  each  yard  was  27  X»  find  the 
cost  price.     Find  the  selling  price. 


222  ARITHMETIC 

16.  Divide  .435  by  .06  and  9.112  by  3.4. 

(a)  (ft) 

.06). 435  3.4)9.112( 

6)43.50  34)91.12(2.68 

7.25  68_ 

231 
204 

272 

(a)  Since  in  this  division  6  is  contained  in  15 
twice  with  remainder  3,  annex  a  zero.  6  is  con- 
tained in  30  5  times. 

(&)  34  is  contained  in  91  units  two  times.  Write 
down  two  and  continue  the  division. 

17.  Divide  15.288  by  .42. 
.42)15.288( 

42)1528.8(36.4 

126  Move  the  decimal   point  two 

268  places  to  the  right  in  both  divisor 

252  ancl    dividend    before    dividing. 

168  Why  can  you  do  this  ? 
168 

18.  Find  the  value  of  : 


.264  -=-.04 

88.76  HH  1:8 

8-H.4 

3.78  -j-.  03 

29.97  +  .37 

12-*-  .06 

14.35  -f-  .05 

2.808  -r-.  45 

3  -;-.25 

4.062  -j-.  06 

59.636  -5-  1.7 

18  -s-  .45 

3.4  -f-.  05 

37.625  -s-  43 

450-^.75 

12.6-5-6 

29.664  H-  .24 

36  -i-  .09 

LESSON  94 

19.  When  do  you   move  the  decimal   point  one 
place   to   the   right    before    dividing  ?     When   two 
places  ?     When   do   you   put   the  decimal  point  in 
your  quotient?     When  do  you  annex  zeros  to  the 
dividend  ? 

20.  If  39  bu.  of  wheat  cost  $34.125,  what  is  the 
price  per  bushel  ? 

21.  At  1.12  a  gallon,  how  many  gallons  of  kero- 
sene can  you  buy  for  $  2.76? 

22.  A  merchant  pays  $240  for  cloth  at  $.75  a 
yard.     How  many  yards  does  he  buy  ? 

23.  A  drover  lost  .045  of  his  flock  of  sheep  by 
wolves,  .125  by  disease,  and  .16  by  theft.     What 
part  of  his  flock  did  he  lose  ?     If  he  sold  the  re- 
mainder, what  part  of  his  flock  did  he  sell  ? 

24.  If  in  question  23  there  were  sold  201  sheep, 
how  many  were  in  the  flock  at  first  ? 

25.  If  a  man  earns  $4.75  a  day,  and  his  average 
daily  expenses  are  $3.40,  in  how  many  days  will  he 
save  $  81  ?     What  is  the  unit  here  ? 


SECTION  XII 


Lesson  95 

1.  The  term  per  cent  (%)  is  used  constantly  in 
business.      The    merchant    gains    20%    on    selling 
cloth,  meaning  by  this  that  he  gains  1 20  on  every 
$  100  that  the  cloth  cost  him.     The  insurance  com- 
pany charges    2%   for   insuring  furniture,  meaning 
that  $  2  is  charged  for  every  $  100  worth  of  furniture 
insured.      A  man  pays  5%  for  the  use  of  money, 
meaning   that   he  pays  $5  a  year   on   every  $  100 
borrowed.     Per  cent  means  hundredths.     50%  of  a 
quantity  is  50  hundredths  of  it. 

2.  A  quantity  divided  into  fourths  is  measured  by 
4  units ;  a  quantity  divided  into  fifths  is  measured 
by  5  units. 

3.  By  how  many  units  is  a   quantity  measured 
that  is  divided  into  sixths  ?    Into  eighths  ?    Tenths  ? 
Twentieths?    Fiftieths?    Hundredths? 

4.  Quantities  considered  in  percentage  are  meas- 
ured by  100  units. 

By  how  many  units  is  \  of  a  quantity,  considered 
in  percentage,  measured  ?     J  ?     j-  ?     %  ? 

224 


LESSON  95  225 

5.    -J  of  a  quantity  equals  what  per  cent  of  it  ?    ^  ? 


50% 


50% 


6.  What  part  of  1  sq.  in.  is  50%  of  it? 

7.  Draw  lines  1  in.,  2  in.,  4  in.,  6  in.,  7  in.  long, 
and  so  on.     Mark  off   50%  of  each  line.     This  is 
what  part  of  each  line  ?     How  many  inches  ?     What 
is  50%  of  6  in.  ?     9  in.  ?     12  in.  ?     6  ft.  ?     18  yd.  ? 
80  yd.  ?     60  mi.  ?     120  mi.  ? 

8.  What  part  of  a  quantity  is  50%  of  it?     How 
many  yards  of  carpet  in  50%  of  120  yd.  ?     What  is 
the  cost  at  50  ^  a  yd.  ? 

9.  Draw  a  2-in.  square  and  mark  off  50%  of  it. 
Draw  an  oblong  4  in.  by  2  in.  and  mark  off  50%  of 
it.     How  many  square  inches  in  50%  of  the  square  ? 
Of  the  oblong? 

10.  A  farmer  gave  his  son   50%   of  his  farm  of 
160  A.     How  many  acres  did  he  receive? 

11.  How  many  inches  in  50%  of  1  ft.?     In  50% 
of   1  yd.?     How  many  quarts   in   50%   of   1   gal.? 
Pints  in  50%  of  1  qt.?     Quarts  in  50%  of  1  bu.  ? 
Quarts  in  50%  of  1  pk.?     Ounces  in  50%  of  1  lb.? 


226 


ARITHMETIC 


Months  in  50%  of  1  yr. 
Minutes  in  50%  of  1  hr.? 
Units  in  50%  of  1  score? 


?     Hours  in  50%  of  1  da.? 
Sheets  in  50%  of  1  quire  ? 


25% 

25% 

25% 

25% 

12.    25%   of   2  sq.  in.  is  what  part  of  it? 
is  what   part?     75%?     100%?     How  many  square 
inches  in  each  case  ? 


13.  A  quantity  considered  in  percentage  is  meas- 
ured by  how  many  units  ?     ^  of  the  quantity  ?     By 
what  per  cent?     75%  is  what  part  of  the  quantity  ? 

14.  Draw  a  line  1  ft.  long  and  divide  it  into  parts 
each  of  which  is  25%  of  1  ft.     Show  75%  of  1  ft. 
What  part  of  1  ft.  is  25%  of  it?  75%  of  it?     How 
many  inches  ? 

15.  Draw  a  square  inch  and  divide  it  into  parts 
each  of  which  is  25%  of  it.     What  part  of  1  sq.  in. 
is  25%  of  it?     50%  of  it?     75%  of  it?     100%  of  it? 
What  part  of  a  quantity  is  25%  of  it?     75%  of  it? 
100%  of  it? 

16.  A  farmer  sold  25%  of  his  flock  of  240  sheep. 
How  many  sheep  did  he  sell  ?     What  per  cent  of  his 
flock  did  he  keep  ?     How  many  sheep  ? 


LESSON  95  227 

17.  A  man  paid  75%  of  $160  for  a  horse.     What 
did  the  horse  cost  ? 

18.  How  many  inches  in  25%  of  1  ft.?     Inches  in 
25%  of  1  yd.?     Quarts  in  25%  of  1  gal.?     Gills  in 
25%   of  1  qt?     Quarts  in   25%  of  1  bu.?     Quarts 
in  25%  of  1  pk.?     Ounces  in  25%  of  1  lb.?     Months 
in  25%  of  1  yr.?     Hours  in  25%  of  1  da.?     Cents  in 
25%  of  $1?     Units  in  25%  of  1  score?     Sheets  in 
25%  of  1  quire? 

How  do  you  find  25%  of  a  quantity? 

19.  Find  75%   of   each   quantity  in  question  18. 
How  do  you  find  75%  of  a  quantity? 

20.  What  per  cent  of  a  quantity  is  J  of  it?     -J-? 
|?     5  f  is  what  part  of  10  ^?     What  per  cent? 

21.  A  grocer  paid  60  ^  a  lb.  for  tea  and  sold  it  so 
as  to  gain   25%  ;   find  the  gain.     Find  the  selling 
'price. 

22.  I  paid  36  f  a  yd.  for  cloth  and  sold  it  at  a  gain 
of  9  ^  a  yd.     What  part  of  the  cost  do  I  gain  ?     What 
per  cent  ? 

23.  If  25%  of  the  cost  of  a  cow  is  $8,  what  did  it 
cost? 

24.  Land  was  bought  at  f  20  an  acre  and  sold  so 
as  to  gain  25%.    Find  the  selling  price. 

25.  A  horse  that  cost  $  80  was  sold  at  a  gain  of 
25%.   Find  the  selling  price. 


228  ARITHMETIC 

26.  If  I  take  off  ^  of  the  marked  price  on  selling 
a  book,  what  per  cent  of  the  marked  price  is  left  ? 

27.  Cecil  had  80^.     He  spent  50%  of  it  to  have 
his  bicycle  mended,  and  25%  of  the  remainder  for 
oranges.     How  much  had  he  left? 

28.  What  per  cent  of  20  f  is  5  fl     Of  16  f  is  8^? 
Of  1  ft.  is  6  in.?     Of  1  da.  is  6  hr.?     Of  1  gal.  is 
Iqt.? 

29.  A  merchant  sold  an  overcoat  at  a  gain  of  $  3, 
which  was  25%   of   the  cost.     What  was  the  cost 
price  ?     The  selling  price  ? 

so.  Roy's  age  is  25%  of  his  father's.  If  Roy  is 
9  yr.  of  age,  how  old  is  his  father  ? 

31.  A  man  who  earns  $240  a  month  spends  75% 
of  it.  How  much  does  he  save  a  month?  How 
much  a  year  ? 

Lesson  96 

1.  J  of  100  units  =  ?     |  of  100  units  =  ?     J  of  a 
quantity  is  what  per  cent  of  it  ?     |-  of  a  quantity  is 
what  per  cent  of  it  ? 

2.  What  part  of  a  line  is  331%  of   it?     Draw 
lines  3  in.,  6  in.,  9  in.,  and  12  in.  long.     Divide  each 
line  into  parts  each  of  which  is  3#l%  of  the  whole 
line.      How  many  inches   in   33^%    of   each  line  ? 
Show  66|%    of   each   line.      How  many  inches   in 
66|%  of  each  line? 


LESSON  96  229 

3.  What   part   of    a   quantity   is    33|-%    of    it? 
66f%   of   it?     What  is  33£%   of  6  ft.?     18   yd.? 
45  mi.  ?     $75?     90  T.  ?     What  is  66f  %  of  each  of 
these  quantities?     100%  of  each? 

4.  How  many  months  in  33J-%  of  1  yr.  ?     Hours 
in  33J%  of  1  da.  ?  Minutes  in  331%  Of  1  hr.  ?  Seconds 
in  33J%  of  1  min.  ?     Find  66f  %  of  each  of  these 
quantities.     100%  of  each. 

5.  331%  of  1  ft.  =  ?    331%  of  1  yd.  =  ?    33J%  of 
1  doz.  =  ?     331%  of  1  quire  =  ?     Find  66f  %  of  each 
of  these  quantities.     100%  of  each. 

6.  Draw  a  3-in.  square  and  a  6-in.  square.    Show 
33J%  and  also  66f  %  of  each.     33|%  of  1  sq.  yd.  =? 
sq.  ft.     66f  %  of  1  sq.  yd.  =  ?  sq.  ft. 

7.  What  part  of  a  quantity  is  equal  to  25%  of  it  ? 
66|%?     75%?     33J%?     100%?     50%? 

8.  What  per  cent  of  a  quantity  is  equal  to  f  of 

it?  j?  f?  i?  |?  |?  |? 

9.  Cloth  which  cost  $.75  a  yard  was  sold  at  a 
loss  of  33 J%.     Find  the  selling  price. 

10.  If   33^%    of   a   cargo   of  flour   consisting  of 
6300   bbl.   was   damaged,   how   many  barrels  -were 
damaged  ? 

11.  A  grain  dealer  invested  $4500  in  wheat,  and 
66|%  of  that  amount  in  oats.     How  much  did  he 
invest  in  oats  ?     In  both  ? 


230  ARITHMETIC 

12.  A  merchant  bought  apples  at  60^  a  bushel, 
and  sold  them  at  a  gain  of  33|%.     Find  the  selling 
price  per  bushel.     Per  peck. 

13.  A  person  gave  $  80  for  one  horse  and  $  75  for 
another.     He  sold  the  first  at  a  gain  of  25%  and  the 
second  at  a  gain  of  33  J%.     Find  his  gain  on  both. 

14.  A  merchant  bought  goods  for  1 120.     He  sold 
half  of  them  at  a  gain  of  33^%  and  the  remainder  at 
a  gain  of  25%.     Find  his  total  gain. 

15.  One   village   has   a  population   of   2000  and 
another  75%  of  that  number.     Find  the  population 
of  the  second  village. 

16.  What  part  of  $6  is  $2?     What   per   cent? 
What  per  cent   of   $24  is  $6?     Of  $24   is  $18? 
Of  16  bu.  is  8  bu.  ?     Of  16  bu.  is  12  bu.  ?     Of  $15 
is  $10?     Of  $36  is  $24? 

17.  What  per  cent  of  1  ft.  is  4  in.  ?     Of  1  yd.  is 
2  ft.  ?    Of  1  sq.  yd.  is  6  sq.  ft.  ?     Of  1  gal.  is  1  qt.  ? 
Of  1  qt.  is  1  pt.  ?     Of  1  bu.  is  3  pk.  ?     Of  1  pk.  is 
6  qt.  ?     Of  1  Ib.  is  4  oz.  ?     Of  1  yr.  is  8  mo.  ?     Of 
1  da.  is  12  hr.  ?     Of  1  dime  is  2  nickels  ?     Of  1  quire 
is  18  sheets  ? 

18.  I  bought  a  rug  for  $24,  and  sold  it  at  an 
advance  of  $8.     Find  the  gain  per  cent.     To  find 
the  gain  per  cent,  you  always  compare  the  gain  with 
what? 


LESSON  97  231 

19.  I  bought  a  cow  for  $28  and  sold  her  for  $35. 
Find  the  gain  per  cent. 

20.  A  dealer  bought  a  bicycle  for  $  60,  and  sold  it 
for  $40.     Find  his  loss  per  cent. 

21.  A  merchant  gains  33^%  by  selling  cloth  at 
an  advance  of  25  ^  a  yard.     Find  the  cost  price  per 
yard. 

22.  A  speculator  lost  $800  by  selling  a  house  at 
25%  below  cost.     Find  what  he  paid  for  it. 

23.  If  66  J%  of  the  population  of  a  certain  town  is 
1800,  find  the  population. 

24.  If  75%  of  the  cost  of  a  farm  is  $  3600,  find  the 
cost. 

Lesson  97 

1.  £  of  100  units  =  ?     |  of  100  units  =  ?     f  of 
100  units  =  ?    |  of  100  units  =  ?    f  of  100  units  =  ? 

What  per  cent  of  a  quantity  is  £  of  it  ?   f  ?   f  ? 

v  v 

2.  Draw  an  oblong  5  in.  long  and  1  in.  wide,  and 
divide  it  into  five  equal  parts.     What  per  cent  of 
the  oblong  is  each  part  ?     Mark  this  per  cent  in  each 
part.     What   per   cent  of   the   oblong   is   2   parts  ? 
3  parts  ?   4  parts  ?   5  parts  ? 

3.  What  part  of  a  quantity  is  20%  of  it?   40%? 
33l%?   60%?   75%?   80%?   100%? 

What  per  cent  of  a  quantity  is  £  of  it  ?  |  ?  f  ?  f  ? 

I?  *?  F  f? 


232  ARITHMETIC 

4.  How  many  cents  in  20%  of  1  dime?     In  40% 
of  1  nickel?     In  80%  of  half  a  dollar?     In  60%  of 
a  25-ct.  piece  ?    How  many  minutes  in  40%  of  1  hr.? 
Seconds  in  00%  of  1  min.?    Sheets  in  75%  of  1  quire? 
Units  in  40%  of  1  score  ? 

5.  If  I  have  5  5-ct.  pieces  and  buy  a  lead  pencil 
for  5  ^,  what  per  cent  of  my  money  do  I  spend  ?     If 
I  spend  15  ^,  what  per  cent  do  I  spend  ? 

6.  A  lady  has  a  piece  of  cloth  containing  16  yd. 
She  cuts  off  12  yd.  to  make  a  dress.     What  per  cent 
of  the  entire  piece  is  required  for  the  dress  ? 

7.  Romney  lost  33^%  of  his  marbles  and  then  had 
16  left.     How  many  had  he  at  first  ? 

8.  Blanche  is  18  yr.  old,  and  Violet  10.     The 
difference   between   their  ages  is  what  per  cent  of 
Violet's  age? 

9.  A  grocer  bought  tea  at  75  ^  a  lb.,  and  sold  it 
for  90  $  a  lb.     Find  his  gain  per  cent.     What  would 
have  been  the  selling  price  to  lose  20%? 

10.  A  man  sold  a  horse  for  f  of  the  cost  price. 
Find  his  loss  per  cent. 

11.  A  merchant  put  2  yd.  of  cloth,  which  sold  at 
$2.50  a  yd.,  on  the  remnant  counter,  and  reduced 
the  price  40%.     Find  the  selling  price. 

12.  Pencils  bought  at  48  ^  a  doz.  were  sold  at  a 
gain  of  25%.     Find  the  selling  price  of  each  pencil. 


LESSON  97  233 

13.  A  grocer  bought  coffee  so  that  he  could  sell  it 
for  36^  a  Ib.  and  make  a  profit  of  331%.     Find  the 
cost  per  Ib. 

14.  A  drover  bought  40  sheep  at  1 6  apiece,  and 
sold  them  at  a  gain  of  20%.     Find  his  gain. 

15.  I  paid  $60  for  one  bicycle  and  $75  for  an- 
other.    I  sold  the  first  at  a  gain  of  33^%  and  the 
second  at  a  loss  of   20%.      Find  my  gain  on  the 
whole  transaction. 

16.  What  is  the  gain  per  cent  when  the  selling 
price  is  1^  times  the  cost  ? 

17.  What  is  the  loss  per  cent  when  the  selling 
price  is  f  of  the  cost  ? 

18.  A  merchant  bought  12  overcoats  for  $  180  and 
sold  them  at  a  gain  of  20%.     Find  the  selling  price 
of  each  coat. 

19.  Bought  pencils  at  24^  a  dozen  and  sold  them 
at  3  ^  each.     Find  the  gain  per  cent. 

20.  A  wholesale   dealer  marks  bicycles  at   $60, 
subject   to  a  discount  of   33^%.     Find   the   actual 
selling  price. 

21.  If   I   buy  600   sheep   at   $5  apiece,  and  pay 
66|%  of  the  cost  price,  how  much  do  I  still  owe  ? 

22.  A  library  has  800  volumes,  of  which  25%  are 
history.     If  50%  of  the  remainder  are  fiction,  how 
many  volumes  of  fiction  are  there  in  the  library  ? 


234 


AKITHMETIC 


23.  A  man  spent  ^  of  his  money  for  a  suit  of 
clothes  and  ^  of  it  for  an  overcoat.  What  per  cent 
of  his  money  did  he  spend  ? 

Lesson  98 

1.  TV  of  100  units  =  ?  ^  of  100  units  =  ? 
T\  of  100  units  =  ?  ^  of  100  units  =  ?  T87  of  100 
units  =  ?  ±$  of  100  units  =  ?  What  per  cent  of  a 
quantity  is  T%  of  it?  ^?  TV?  TV?  ft? 


10% 

10% 

10% 

io,% 

10% 

10% 

10% 

10% 

10% 

10% 

2.  What  part  of  this  oblong  is  10%  of  it?  20%  ? 
?    40%.?    50%?    60%?    70%?    80%?    90%? 

*7 

3.  What  per  cent  of  this  oblong  is  J  of  it  ?     ^  of 

^     iW     t?     iV?     T9o"?     f? 

4.  How  many  cents  in  10%  of  1  dime?     In  30% 
of  $1  ?     In  30%  of  half  a  dollar?     How  many  days 
in  10%  of  the  month  of  June?     Seconds  in  30%  of 
1  min.  ?     Units  in  90%  of  1  score? 

5.  A  farmer  raised  360  bu.  of  wheat,  and  kept 
10%  of  this  for  flour  for  his  own  family.     How  many 
did  he  sell  ? 


LESSON  98 


235 


6.  A  man  saves  each  month  10%  of  his  salary. 
If  this  is  1 22,  what  is  his  salary  ? 

7.  If  10%  of  a  boy's  rate  of  walking  is  ^  mi.  per 
hr.,  what  is  his  rate  per  hr.  ? 

8.  A  boy  saved  $40  in  one  year,  and  the  next 
year  he  saved  10%  more  than  that.     How  much  did 
he  save  in  2  yr.  ? 

9.  A  house  rents  at  $300  a  year,  which  is  10%  of 
its  value.     What  is  the  house  worth  ? 

10.    1  of  100  units  =  ?     J  of  100  units  =  ?     f  of 
100  units  =  ?     What  per  cent  of  a  quantity  is  -^  of 

it?    ? 


121% 

12}  % 

12*% 

121% 

12}% 

12*  % 

12}  % 

12}  % 

11.  What   part   of   this   oblong   is    12J%    of  it? 
What  per  cent  of  this  oblong  is  J-  of  it?     £?     %? 

t?  t? 

12.  What  part  of  any  quantity  is  12J%   of   it? 
What  per  cent  of  any  quantity  is  -|-  of  it  ? 

13.  How  many  inches  in  12|%  of  1  ft.  ?     Square 
inches  in  121%   of  l  sq.  ft.?     Pints   in    12J%    of 
1   gal.?     Quarts   in   12J%    of   1   bu.  ?     Ounces   in 


236 


ARITHMETIC 


12|%  of  1  Ib.  ?     Hours  in  12J%  of  1  da.  ?     Sheets 
in  12-       Of 


14.  Four  pupils  of  the  first  grade  were  absent 
Monday.     If  this  was  12  J%  of  the  whole  number, 
how  many  are  in  the  first  grade  ? 

15.  One-eighth  of  a  box  of  oranges  was  found  to 
be  decayed  on  opening  the  box.     What  per  cent  of 
the  oranges  was  good  ? 

16.  A  laboring  man  is  idle  2  da.  out  of  8.     What 
per  cent  of  the  time  is  he  idle  ? 

17.  A  fruit  dealer  buys  pineapples  at  8^  apiece, 
and  sells  them  at  9  ^  apiece.     Find  his  gain  per  cent. 

18.  What  is  £  of  100%?     f  of  100  ? 


19.  What   part   of  this   oblong   is   16  J%   of  it? 
What  per  cent  of  this  oblong  is  £  of  it  ?    £  ?    f  ?    f  ? 

20.  How  many  inches  in  16|%  of  1  ft.  ?     Inches 
in  16f  %  of  1  yd.  ?     Square  inches  in  16f  %  of  1  sq. 
ft.  ?     Hours  in  16f  %  of  1  da.  ?     Minutes  in  16|% 
of  1  hr.  ?     Months  in  16|%   of  1  yr.  ?     Sheets  in 
16|%  of  1  quire? 


LESSON  99  237 

21.  What    is    the    difference    in    hours   between 
16f  %  and  12J%  of  one  day? 

22.  What  per  cent  of  1  gal.  is  1  pt.  ?     Of  1  qt.  is 
1  pt.  ?     Of  1  da.  is  4  hr.  ?     Of  1  yr.  is  8  mo.  ?     Of 
1  quire  is  18  sheets  ?     Of  1  score  is  8  units  ? 

23.  Mrs.  Hume  spent  $  4  for  a  chair  and  $  28  for 
a  rug.     What  per  cent  of  the  whole  sum  did  the 
chair  cost  ? 

24.  If  the   price   of   flour   advances  from  $5  to 
$5.50  a  bbl.,  what  is  the  per  cent  of  increase? 

25.  A  fruit  dealer  buys  oranges  at  8^  a  doz.,  and 
sells  them  at  1  ^  apiece.     Find  his  gain  per  cent. 

Lesson  99 

1.  Find    the    quantity   of   which  $2   is   12J%. 
$.08  is  50%.     12.50  is  16f  %.     £  pt.  is  25%.     6  bu. 
is  66f  %.     12  mi.  is  75%.     12  mi.  is  60%. 

2.  What   is   meant   by  saying  that   12J%=|-? 
16J#=*?      i  =  33i%?      66f%=f?      |=75%? 
100%  =1? 

3.  What  per  cent  of  1  Ib.  Avoir,  is  12  oz.  ?     Of 
1  quire  is  18  sheets  ?     Of  1  da.  is  8  hr.  ?     Of  1  yr. 
is  6  mo.?     Of  $1  is  20^? 

4.  What  is  the  ratio  of  25%  of  a  quantity  to 
75%  of  it?     Of  75%  to  25     ?     Of  33J%  to  66f%  ? 
Of  80%  to  20%?     Of  20%  to  80%?     Of  16|%  to 


238  ARITHMETIC 

% 

331%  ?     Of  33^%  to  16f  %  ?     Of  60%  to  40%  ?     Of 
40%  to  60%? 

5.  In  a  certain  school   33^%    of  the  pupils  are 
boys,  and  there  are  28  girls.     Find  the  number  of 
boys. 

6.  A  young  man  spends  40%  of  his  salary;  what 
per  cent  does  he  save  ?     If  he  spends  $  24  a  month, 
what  does  he  save? 

7.  A  kitchen  range  burns  50%  of  1  T.  of  coal  a 
month.     How  many  tons  does  it  burn  in  one  year  ? 

8.  A  man  sold  a  cow  that  cost  $  36  at  a  loss  of 
25%.     Find  the  selling  price. 

9.  A  young  man  put  1 64  in  a  savings  bank  and 
soon  after  drew  out  12^%  of  it.     How  much  still 
remained  in  the  bank? 

10.  From  a  5-gal.  can  of  oil  2  gal.  are  drawn  out. 
What  per  cent  still  remains  in  the  can? 

11.  What  per  cent  is  lost  by  selling  goods  at  |  of 
the  cost  ?     At  |  of  the  cost  ? 

12.  What  per  cent  is  gained  by  selling  goods  at  | 
of  the  cost?     At  |  of  the  cost? 

13.  25%  of  the  number  of  bushels  of  grain  raised 
by  a  farmer  are  oats  and  50%  wheat.     If  he  raises 
320  bu.  of  oats,  how  many  bushels  of  wheat  does  he 
raise  ? 


LESSON  99  239 

14.  A   young  man   in   the    High   School   studies 
at  home  12  \%  of  the  entire  day.     How  many  hours 
does  he  study  at  home  each  day  ? 

15.  A  merchant  buys  60  yd.  of  silk  for  $  180  and 
sells  it  at  an  advance  of  20%.     Find  the  selling  price 
per  yd. 

16.  A  man  paid  $  150  for  a  horse  and  50%  more 
for  a  carriage.     Find  the  cost  of  both. 

17.  What  per  cent  is  gained  if  cloth  costing  30  ^  a 
yard  is  sold  for  40^?     36^?     42/?     35^?     50^? 

18.  What  per  cent  is  lost  if  cloth  bought  at  36  1  is 
sold  for  27^?     30^? 


19.  If  hats  are  bought  at  $2.50  and  sold  for  $3 
apiece,  find  the  gain  per  cent. 

20.  Eggs  bought  at  $  3  a  crate  of  30  doz.  are  sold 
at  12  ^  a  dozen.     Find  the  gain  per  cent. 


SECTION  XIII 

Lesson  100 

1.  Name  five  different  units  of   length  that  will 
exactly  measure  a  line  12  in.  long.     What  is  the 
ratio  of  the  line  to  the  6-in.  unit? 

2.  I  owe  a  debt  measured  by  the  number  8  and 
the  unit  $5.     How  many  ten-dollar  bills  will  pay 
the  debt?     What  is  the  ratio  of  the  debt  to  $  10? 

3.  A  fruit  dealer  arranges-  his  apples  in  piles  of 
4  for  5  $.     If  he  sells  1  pile  to  each  of  6  customers, 
how  many  apples  does  he  sell  ?     For  how  much  ? 

4.  If  the  measuring  unit  is  a  line  3  in.  long,  draw 
the  line  made  up  of  three  parts,  the  first  being  3 
times,  the  second  4  times,  and  the  third  5  times  the 
measuring  unit  ?     How  many  inches  in  the  line  ? 

5.  What  is  the  quantity  which  is   equal  to  the 
sum  of  5,  3,  and  6  times  the  measuring  unit  ? 

6.  A  fruit  dealer  sells  his  apples  at  the  rate  of 
6  for  5  f.      He  sold  five  cents'  worth  to  each  of  9 
customers.     How  many  apples  did  he  sell  ? 

240 


LESS,*'   100  241 

7.  A  horse  which  travels  at  the  rate  of  6  mi. 
an  hour  goes  from  A  to  B  in  2  hr.,  and  from  B  to  C 
in  3  hr.     How  long  is  the  road  from  A  to  C  ? 

8.  Find  the  number  of  times  that  a  clock  strikes 
from  8.30  A.M.  until  2.30  P.M.,  if  the  clock  strikes 
every  hour. 

9.  A  man  left  to  his  widow  §8350,  to  his  son 
1 6425,  and  to  his  daughter  $ 5725.     Find  the  value 
of  his  property. 

10.  Find  the  capacity  of  four  bins,  the  first  of 
which  will  contain  65.223  bu.,  the  second  34.542  bu., 
the  third  20.112  bu.,  and  the  fourth  19.123  bu.     If 
these  four  bins  are  full  of  wheat,  what  is  it  worth  at 
$  1  a  bushel  ? 

11.  A  merchant  sold  122  yd.  of  cloth  from  a  piece 
containing  150  yd.     What  is  the  remainder  worth 
at  ft. 50  a  yd.? 

12.  What  quantity  is  the  difference  between  the 
numbers  6  and  2,  the  unit  being  $  5  ?     8 10?     1 20? 

13.  How  much  greater  are  6  units  of  $  9  than  5 
units  of  $  10  ?     What  is  the  ratio  of  this  difference 
to  the  unit  $  2  ? 

14.  A  car  containing  24  T.  of  coal  was  divided 
between  two  families.     If  the  first  got  11.25  T.,  how 
many  did  the  second  get  ? 

15.  Find  the  number  of  square  feet  in  an  oblong 
garden  12  yd.  long  and  9  yd.  wide. 


242  ARITHMETIC 

16.  Two  vessels  start  from  the  same  point   and 
travel  down  stream,  the  first  at  the  rate  of  12  mi.  an 
hr.  and  the  second  at  the  rate  of  8  mi.  an  hr.     How 
far  apart  will  they  be  in  6  hr.  ? 

17.  If  these  two  vessels  travel  in  opposite  direc- 
tions at  the  same  rate,  how  far  apart  will  they  be  in 
6  hr.  ?     Mark  off  a  line  to  represent  this  distance  ? 

18.  A  speculator  bought  5  lots  at  $600  each,  and 
4  lots  at  $ 500  each.     He  sold  them  for  $  575  apiece. 
Find  his  gain. 

19.  Find  the  weight  of  a  block  of  wood  3  ft.  long, 
2  ft.  wide,  and  1  ft.  thick,  weighing  32.5  Ib.  per 
cu.  ft. 

20.  A  drover  bought  8  sheep  at  $5.35  per  head, 
and  17  at  $4.25.    Find  the  total  cost.    Find  his  gain 
on  selling  them  for  $  150. 

Lesson  101 

1.  A  string  36  in.  long  has  a  piece  4  in.  long  cut 
off,  and  then  another  piece  of  the  same  length,  and 
so  on.     How  often  can  this  be  done  ?     What  is  the 
unit  here  ? 

2.  In  question  1,  what  is  the  ratio  of  the  length  of 
the  string  to  that  of  the  unit  ?     Of  the  length  of  the 
unit  to  that  of  the  string  ? 

3.  Divide  $  24  between  A  and  B,  giving  B  3  times 
as  much  as  A.     What  is  the  unit  here? 


LESSON  101  243 

4.  Divide   1 30   between  A,  B,  and  C,  giving  B 
twice  as  much  as  C,  and  A  1J  times  as  much  as  B. 
What  is  the  unit  here  ? 

5.  A  merchant  sold  cloth  at   $1  a  yd.,  and  an 
equal  quantity  at  1 2  a  yd.      What  did   1    yd.   of 
each  sell  for?     If  all  the  cloth  sold  for  $24,  how 
many  yards  of  each  did  he  sell  ?     What  is  the  unit 
here? 

6.  A  merchant  sold  silk  at  $ 2  a  yd.,  and  an  equal 
quantity  at  13  a  yd.     If  all  the  silk  sold  for  $80, 
how  many  yards  of  each  did  he  sell  ?     What  is  the 
unit  here  ? 

7.  A  township  is  6  mi.  square.     Draw  a  town- 
ship, making  1  in.  for  1  mi.     What  is  its  area  ? 

8.  A  township  is  divided  into  36  sections,  each 
1  mi.  square.     Divide  the  township  you  have  drawn 
into  36  sections.     How  many  square  inches  in  your 
drawing  represent  one  section  ? 

9.  Each  section  of  one  square  mile  contains  640  A. 
Divide  one  section  into  4  farms  of  160  A. 

10.  What  is  the  difference  in  area  between  a  6  in. 
square  and  an  oblong  containing  6  sq.  in.? 

11.  Into  how  many  townships  can  a  tract  of  land 
12  mi.  square  be  divided  ? 

12.  What  is  the  ratio   of   20  min.   to  1  hr.?     A 
train  runs  15  mi.  in  20  min.     At  the  same  rate  how 
far  would  it  go  in  1  hr.? 


244  ARITHMETIC 

13.  Soap  that  cost  4  f  a  cake  is  sold  for  5  ^.      The 
gain  is  what  part  of  the  cost?     What  per  cent  of 
the  cost? 

14.  If  3  ft.  is  the  unit  of  length,  what  is  the  unit 
of  area  ? 

15.  Divide  $  48  between  Julian  and  Alder  so  that 
Julian  may  get  $  3  for  every  $  1  Alder  gets.    What  is 
the  unit  here  ? 

16.  Roy  has  24  marbles,  and  Cecil  6.     They  play 
together,  and  Roy  loses  \  of  his.      How  many  has 
Cecil  now? 

17.  Draw  a  line  10  in.  long.     Measure  it  with  a 
unit  J  ft.  long.     How  many  times  did  you  measure  ? 
10.  in.  is  equal  to  f  ft.     What  is  the  unit  here? 
What  is  the  number? 

18.  Draw  a  line  9  in.  long.      Measure  it  with  a 
unit  \  ft.  long.     How  many  times  did  you  measure  ? 
9  in.  is  equal  to  f  ft.    What  is  the  unit  here  ?    What 
is  the  number  ? 

19.  Name  the  units  that  measure  the  following 
quantities   and   give   the   number   of  units  :    f  ft., 
|  yd.,  |  yd.,  f  f,  |  lb.,  1£  da.,  f  hr.,  |  bu.,  f  wk., 
^  quire,  and  -^  score. 

20.  What  part  of  a  dollar  is  needed  to  give  \  of  a 
dollar  to  each  of  4  persons  ?     What  is  the  number 
here  ?     The  unit  ?     The  quantity  ? 


LESSON  102  245 

21.  What  quantity  is  measured  by  the  number  12 
and  the  unit  |  ft.  ? 

22.  What   quantity  is  measured  4  times  by  the 
unit  \  wk.  ? 

23.  How  often  does  the  unit  £  bu.  measure  the 
quantity  |  bu.? 

24.  What  is  the  unit  that  measures  the  quantity 
f  Ib.  3  times  ? 

Lesson  102 

1.  George  gives  away  J  of  his  marbles  and  has 
16  left.     How  many  had  he  at  first  ? 

2.  A  paid  $40  an  acre  for  a  farm.     This  was  ^  of 
what  B  paid  an  acre  for  his  farm.     What  did  B  pay 
for  his  farm  of  60  A.? 


3.  A  man  earns  $  3|  a  day,  and  his  daily  expenses 
are  $  1  J.     In  how  many  days  will  he  save  enough  to 
buy  a  bicycle  costing  $  60  ? 

4.  Bought  tea  at  75  ^  a  Ib.  and  sold  it  at  a  gain 
of  331%.     Find  the  selling  price. 

5.  James  received  a  present  of  $  24.     He  gave  ^ 
of  it  to  his  sister,  and  J  of  the  remainder  to  his 
brother,  and  kept  the  rest  himself.     How  much  did 
each  receive  ? 

6.  How  many  pounds  of  butter,  worth  $  .21  a  Ib., 
will  cost  120.58? 


246  ARITHMETIC 

7.  If  a  man  eats  32  oz.  of  bread  in  one  day,  how 
many  pounds  will  he  eat  in  one  week  ? 

8.  Two  farmers  go  to  market.     The  first  has  36 
bu.  of  wheat  weighing  60  Ib.  a  bu.,  and  the  second 
48  bu.  of  oats  weighing  32  Ib.  a  bu.     Which  load  is 
heavier  and  how  much  ? 

9.  What  will  12  bu.  30  Ib.  of  wheat  cost  at  $  .84 
a  bu.  ?     What  will  15  bu.  8  Ib.  of  oats  cost  at  $  .36 
abu.? 

10.  A  farmer  sold  6  loads  of  wheat,  each  contain- 
ing 32  bu.,  at  8.94  a  bu.     Find  the  total  selling 
price. 

11.  Find  the  cost  of  laying  a  cement   sidewalk 
30  yd.  long  and  4  ft.  wide,  at  16  f  a  square  foot. 

12.  A  house  worth  $4800  is  insured  for  75%  of 
its  value.     For  what  is  it  insured  ? 

13.  A  manufacturer  employed  25  men,  paying  on 
the  average  $1.50.     What  will  it  cost  him  a  day  to 
increase  their  wages  10%? 

14.  Of  30  pupils  in  a  grade  3  were  not  promoted. 
What  per  cent  of  the  class  failed  to  be  promoted  ? 

15.  A  lady  is  27  years  of  age.     If  her  age  is  75% 
of  her  husband's,  how  old  is  he  ? 

16.  A  lady  spent  66|%  of  the  money  in  her  purse 
for  furniture,  16 -|%  for  carpet,  and  the  rest  for  a 
Jacket.     What  per  cent  did  she  spend  for  a  jacket  ? 
If  this,  was  $  25,  how  much  had  she  at  first  ? 


LESSON  103 


24T 


17.  A  dressmaker  has  12  dresses  to  make.     If  she 
makes  33  J%  of  them  in  12  da.,  how  many  days  will 
she  take  to  make  them  all  ? 

18.  I  bought  6  doz.  lemons  at  $.20  a  doz.,  and 
sold  them  for  2  f  each.    What  was  my  gain  per  cent  ? 

19.  A  man  had  $  6000  in  the  bank.     He  drew  out 
50%  of  it  and  bought  a  house  with  75%  of  the  sum 
drawn  out.     Find  the  cost  of  the  house. 

20.  In  a  school  there  are  42  pupils ,  the  ratio  of 
the  number  of  boys  to  the  number  of  girls  is  3  to  4. 
How  many  of  each  ? 


Lesson  103 

l.  Write  down  neatly  the  following  statement  of 
six  weeks'  cash  receipts ;  add  the  amounts  vertically 
and  find  the  sum  of  the  totals  : 


MON. 

TUBS. 

WED. 

THUR. 

FKI. 

SAT. 

1st 

$26.53 

$32.15 

$36.21 

$28.06 

$25.84 

$45.63 

2d 

21.78 

28.28 

31.43 

32.60 

27.97 

44.55 

3d 

18.66 

24.12 

26.55 

27.13 

24.95 

41.16 

4th 

26.94 

35.92 

32.19 

36.08 

22.31 

48.29 

5th 

16.23 

31.14 

35.56 

32.23 

29.99 

54.93 

6th 

19.20 

25.05 

24.97 

29.67 

24.15 

60.03 

TOTAL 

248  ARITHMETIC 

2.    Add  as  in  question  1  : 


Mox. 

TUBS. 

WED. 

THUR. 

FRI. 

SAT. 

1st 

$54.73 

$35.71 

$68.68 

$37.69 

$  53.44 

$67.41 

2d 

46.17 

65.41 

34.76 

62.07 

61.16 

52.61 

3d 

45.80 

57.29 

42.63 

71.28 

68.72 

67.43 

4th 

47.47 

60.50 

78.25 

63.36 

45.76 

43.80 

5th 

64.52 

39.65 

45.38 

15.75 

32.74 

74.45 

6th 

52.41 

43.77 

58.97 

42.57 

41.78 

65.28 

TOTA  L 

3.    Add  as  in  question  1 : 


MON. 

TUBS. 

WED. 

THUR. 

FRI. 

SAT. 

1st 

$86.93 

$76.19 

$67.60 

$74.61 

$69.65 

$68.29 

2d 

93.47 

68.37 

86.43 

64.62 

57.42 

74.95 

3d 

64.55 

76.04 

53.86 

65.02 

69.38 

78.54 

4th 

97.98 

93.57 

64.36 

59.41 

23.45 

96.71 

5th 

62.67 

86.21 

68.15 

62.39 

46.29 

76.58 

6th 

49.78 

46.53 

76.28 

78.35 

95.43 

93.75 

TOTAL 

Add: 

4. 

6134 

9268 

3257 

2168 

8497 

5769 

7931 

8394 

4758 

3275 

4528 

5486 

2738 

4623 

2832 

9034 

4243 

2752 

4654 

9657 

LESSON  103 


249 


5.   25146 

67125 

92745 

9829 

878 

35924 

58797 

4572 

57436 

6543 

27639 

25372 

462 

44444 

31819 

6.  34 

58 

52    78 

39    69 

15 

47 

93    73 

86    93 

75 

29 

35    28 

64    82 

;   62 

97 

67    89 

26    45 

28 

32 

63    83 

97    37 

99 

49 

68    44 

36    66 

95 

78 

81    60 

99    58 

32 

52 

39    33 

78    87 

57 

91 

42    56 

64    62 

43 

47 

55    78 

76    63 

7. 

6958.994 

7936.042 

6683.145 

8772.343 

7721.358 

948.03 

5822.962 

2546.563 

7364.207 

7319.526 

7864.289 

4563.09 

8393.751 

7325.004 

7825.4 

Subtract  : 

8. 

$3862.93 

$6760.68 

$1696.65 

1391.76 

$3976.98 
1678.63 


1098.91 

$2035.68 
364.76 


43.68 

$1948.39 
1754.46 


250 


ARITHMETIC 


10. 


11. 


12. 


13. 


14. 


15. 


16. 


17. 


18. 


19. 


20. 


21. 


22. 


83559.83 


$4264.15 


§1763.29 


1932.57 
15436.29 

1268.34 

$2678.28 

685.38 

$1180.66 

4963.19 
12016.72 

312.83 

$8416.60 

119.25 
$5300.20 

1215.17 
$1732.25 

1542.24 
$4656.20 

2223.42 

$1097.47 

1214.03 
$3661.00 

738.75 
$1201.60 

1024.74 
$1850.14 

1139.67 
24375 

311.20 

95657 
6478 

49328 
1760 

205639 

196.17 
16125 

14692 

84329 
59761 

819634 

5765 

29845 
14008 

726998 

497256 

337.877 
199.601 

56.979 

174593 

698.206 
587.964 

34.702 

395432 
279.345 

158.709 
632.194 

28.034 
84.67 

15.96 
49.107 

576.4 
56.5 

19.483 

158. 

28.315 
223. 

26.548 

599.78 
64.532 

77.065 

36.427 
382.635 

1.89 

32.808 

13.284 

12.08 

49.17 

LESSON  104 

251 

-3          392« 

45.652 

445.2 

1.473               18.654 

159.304 

„<        171.8' 

672.39 

239.76 

25.631                 43.1 

173.291 

Lesson  104 

Multiply  : 

l.          456 
32 

439            862 
_25              85 

676            864 
68              96 

2.    155.76 
28 

162.24      134.36 
48              43 

$76.82      $46.29 
15             75 

3.    157.06 
13 

167.82      $43.85 
26              58 

$60.09      $39.95 

88              63 

4.      57261 

38 

89437         65435 
^5              48 

23826        16436 
73              84 

5.         653 
231 

429            384 
324             256 

629            439 
125            121 

6.          307 

268 

255            460 
199             121 

720            840 
340            350 

7.         907 

359 

707            796 

660            263 

129            930 

888            725 

8.       1495 
236 

1598          2716 
426            287 

3948          5048 
635            650 

252  ARITHMETIC 


9. 
10. 
11. 
12. 
13. 
14. 
15. 
16. 

3526 

819 

1521 

637 

6432 

568 

$18.64 
253 

9780 
876 

1946 

621 

$64.32 
321 

$32.34 
125 

$84.50 
212 

$13.67 
631 

$63.51 

208 

$17.01 

784 

$83.95 
214 

$22.35 
523 

$38.26 
350 

$26.57 
801 

$68.91 
141 

$11.51 

189 

$14.93 
276 

$39.03 

168 

$90.75 
324 

$34.26 

275 

$64.29 
343 

$35.28 
653 

$42.86 
797 

42.57 
375 

6.293 
435 

8.764 
423 

1.534 
264 

9.12 

258 

.295 
147 

.375 
294 

.826 
131 

6.293 
219 

2.03 
145 

115.5 

818 

3.064 
513 

48.18 
155 

585.3 
306 

4.659 
314 

In  the  following  questions  name  the  trial  divisors 
and  find  the  quotients  and  remainders : 

17.  32)4985  52)2735  61)6751  43)8668 

18.  49)3548  66)5675  54)2085  19)5921 

19.  36)6772  87)5439  73)9106  99)6487 

20.  212)2524  314)7768  425)3467  512)5394 


LESSON  104  253 

21.  108)5695   219)9488   706)9983  822)7786 

22.  198)9897   299)3428   384)7534  795)2857 

23.  346)67894  578)17639  289)33333  684)46999 

24.  563)26407  662)40640  147)68952  365)41707 

25.  839)17788  777)18810  556)79964  319)68795 


ANSWERS 


Lesson  58 
12.  11  £  15.  $19,  $31,  50^,  68  £  16.  31  £  17.  4^ 

Lesson  60 

3.  81,  60,  91,  110,  121,  101,  119,  112.  4.  697,  861, 
751,  811,  920,  1221.  5.  969,  719,  871,  917,  811,  1181. 

6.  68,  95,  41,  90,  71,  50,  51,  101.    7.  23,  33,  13,  32,  36, 
48,  48,  35.   8.  632,  562,  80,  238,  344,  709.    9.  $  390. 
10.  $1.11.    11.  $125.    12.  $2.35.    13.  $1091. 

14.  $991. 

Lesson  61 

5.  41  £  7.  60,  62,  95,  127,  82,  120,  122,  111.  8.  982, 
1000,  1229,  729,  802,  920,  929.  9.  981,  828,  1121,  990, 
1100,999,1110.  10.  71  £  11.  237,258,342,315, 
413,  532,  733.  12.  2222,  3210,  1023,  2626,  1061,  1802. 
13.  5336,  5104,  3015,  2050,  6591,  89.  14.  872. 

15.  $1365.   16.  $1220.   17.  91  da.,  92  da. 

Lesson  62 

5.  72  £    6.  61,  83,  81,  102,  103,  132,  138,  138. 

7.  783,  919,  923,  1369,  1383,  1113,  837,  1112.   8.  $1.22. 
9.  1068,  629,  1099,  732,  1332,  1110,  1182,  810.   10.  443, 
131,  164,  282,  63,  494,  156,  257.    11.  4304,  2202,  4013, 

255 


256  ANSWERS 

6033, 1113,  4004,  4150,  1000.     12.  1214,  4990,  1382, 
661,  1324,  941,  2548,  2423.    13.  $  705.     14.  1905^ 

15.  $1190.   16.  $1000.   18.  $65. 

Lesson  63 

10.  524, 1023, 1696,  2605,  1015, 1565.  13.  120  mi. 
22.  32. 

Lesson  64 

10.   792,  1188,  1584,  1980,  2376,  3036.  13.   $  2250. 

16.  25,  54,  76,  49,  67,  122.       17.  288,  192,  144,  130,  144, 
139.      18.   176,  117,  147,  64,  56,  51.       19.   99,  66,  65,  52, 
63,56.      21.   102  bu.      22.   $200,  $40. 

Lesson  65 

14.  $  9.87,  $  59.37,  $  846.48,  $  6329.86.  15.  $  62.69, 
$888.18.  16.  $38.59.  17.  $  5.33,  $41.32,  $  41.31, 
$  1133.11.  18.  $  11.25.  19.  $  2.35.  20.  $  15.69,  $  88.60, 
$  157.55,  $  1280.52.  21.  $  39.75.  22.  $  24.13,  $  27.50, 
$  .23,  $  .03,  $  125.75,  $  80.65.  23.  $  248.65.  24.  $  11.20. 

Lesson  66 
3.  2  gal.  2  qt.  1  pt.      15.  6/,  3/,  45/,  69/. 

Lesson  67 

1.  8  gal.  1  qt.  4.  1  gal.  3  qt.  5.  Sf,  48^.  12.  8  gal. 
2qt,  17  gal.  13.  27  Ib.  14.  96?,  4£  15.  4  wk. 
16.  36  ^.  18.  12  /.  20.  $  15.  21.  Dime,  nickel,  and 
penny. 


ANSWERS  257 

Lesson  68 

1.  16  qt.  1  pt.  2.  99  £  3.  39  £  5.  5J  hr.,  26 \  hr. 
10.  174  mi.  12.  $234.  13.  $52.  16.  45^.  18.  2  gal. 
3  qt.  1  pt.  19.  14.  22.  20  mi. 

Lesson  69 

5.  $21.   6.  $74.   7.  59,92,134,133,141,84,132, 
129.    8.  415,  709,  822,  803,  741,  1201,  1444,  1384. 

9.  949,  1498,  1535,  1174,  1202,  1454,  900,  910.   11.  144. 
12.  996.    13.  432,  404,  182,  530,  183,  451,  43,  243. 
14.  4104,  6912, 909,  3991, 1095,  526,  3778,  4913,  818,  3651. 
16.  66.   17.  26  mi. ;  23  mi.   ia  514  A.   19.  $  64.75. 
20.  $  46.50.   21.  $  63,  $  21.   22.  24. 

Lesson  70 

6.  $  41.25.   7.  62  Ib.   8.  75,  139,  122,  124,  135,  90, 
133,  155.   9.  661,  872,  653,  1443,  1415,  1223,  652,  1201. 

10.  976, 1588, 1445, 924, 842, 1578, 1328, 1522.  11.  115  mi. 
12.  120  mi.   13.  431,  262,  343,  161,  297,  406,  175,  158. 

14.  3621,  786,  2625,  4426,  1866,  1628,  5788,  1888. 

15.  256  A.  16.  18  £  17.  $1050.  18.  9£   19.  $675. 
20.  131  days. 

Lesson  71 

5.  8 ;  5 ;  14 ;  8  ;  12.  6.  6  in.  7  5  gal.  9.  1824, 
2905,  4170,  6615,  6986,  4704.  11.  $  3192.  13.  42,  26, 
73,35.  15.  63^.  16.  24bbl.  17.  25?.  18.  92^. 

Lesson  72 

5.  $9.50.  6.  $50.  7.  $  12.60,  $  40.45,  $  13.14, 
$17.92,  $31.68.  8.  1744.  9.  $2848,  $356. 


258  ANSWERS 

10.  $  246,   305,   356,  873  bu.        11.   176  A.        12.  274. 
13.   $1.28.       17.   60  £       23.   44^,  3qt.        24.   24  times. 

Lesson  73 

4.  19  qt.,  46  qt.,  60  qt.,  32  qt.,  96  qt.,  164  qt.  5.  48  qt., 
112  qt.,  72  qt.,  20  qt.,  30  qt.  6.  11  pk.,  92  qt,  116  qt., 
131  qt.  7.  1  lb.,  8  lb.,  94  Ib.  8.  1  bu.,  210  lb. 
10.  11  bu.,  41  bu.,  libu.,  90^.  11.  75  lb.  13.  24  oz., 
44  oz.,  58  oz.,  \  lb.,  i  lb.,  f  lb.,  TV  lb.,  $  lb.,  T5¥  lb.  14.  4  £ 
15.  76  oz.  16.  52  oz.,  70  oz., 


Lesson  74 
16.   720.        17.   231  cu.  in.        18.   8000  oz.        19.   6  lb. 

20.   96  sq.  in. 

Lesson  75 

16.  CX,  CXL,  CXLIX,  CL,  CLIV,  CLXXXII,  CXC, 
CXCIV.  17.  CCC,  XV,  CCCXV;  CC,  LXXXIV, 

CCLXXXIV;  D,  XCIX,  DXCIX;  DCXIV,  DCCXXXIX, 
DCCCXXVII,  DCCCCXXXIV.  18.  M,  CCL,  MCCL; 
CCCXLIV,  MCCCXLIV;  MDCCCXCVIII,  MCCCCXC1I. 

Lesson  76 

3.  $18.  5.  $15.  6.  $21,  $24,  $11.  7.  20^. 
8.  The  latter,  l£  11.  $10,  $70.  12.  $16,  $15, 
$  24,  8  lb.,  6  lb.,  24  lb.  13.  15  gal.,  16  gal.,  18  gal., 

15  yd.,  35  yd.,  21  yd.  14.  12  yd.,  6  yd.,  none.  16.  i, 
48  £  18.  28^.  19.  i,  3.  22.  £;  5;  540  lb. 

23.   $  3.60.       24.   90  mi. 

Lesson  77 

16.  64  pt.,  24  pt.,  16  pt,  8  pt.,  \  gal.,  40  pt.,  |  gal. 
17.  40  pt.,  f  gal.  22.  40  yr. 


ANSWERS  259 

Lesson  78 

2.  A,  T87T>  A>  A»  T3o>  A  lb-     3-  T3o  ib.,  20  f.  5.  $  T<v, 

90  ^  10  £         6.  1  cent,  1  nickel,  or  1  dime.  15.   f  ,  |, 

2A,  5«,  1A>  H>  7H>  2^.  16.  i,  i, 


19.   $2|.       20.   $3J. 

Lesson  79 

1.  $  9.  5.  T\,  A,  $  6000.  7.  if,  A,  15°  A- 
8.  60  da.  14.  |,  {.  15.  240  A.,  90  A.,  60  A.,  90  A. 
18.  TV,T3o,  $30. 

Lesson  81 

1.  21  gal.  2.  2  lb.  6  oz.  3.  1  in.,  30,  No.  4.  7, 
f  3.50.  5.  400  yd.,  $  24,  $  96.  6.  $  4.80.  7.  6  yd. 
3  in.  8.  42  A.  9.  2  mi.,  4  sq.  mi.  10.  6  lb.,  70  lb. 

11.  $77.       12.   32  lb.        13.   24yd.,  4yd.       14.   60  lb., 
40  lb.       15.   $  3.60.       16.   $  4.80.       17.   6  mi.,  36  sq.  mi. 
18.   44  strips,  2  ft.       19.   4  bu.  3  pk.       20.  40  mi.  an  hr. 
21.   30  mi. 

Lesson  82 

4.  34,  40,  37,  62,  80,  86,  97,  108.     5.   $  126.20,  $  69.36, 
$  98.30,  $  134.35,  $  528.98,  $  667.70,  $  8841.60,  $  4668.08. 
6.   $  572.24,  $  670.91,  $  1409.52,  $  755.06.     7.   $  624.52. 
8.   72  bu.,  $  72.85.        9.   $  7.95,  $  8.88,  |  59.49,  $  276.99. 
10.   $  108.47,  $  1569.85,  $  696.97,  $  2255.43.       11.   $  495. 

12.  $24.25.         13.   $8.83.         14.   12  lb. 

Lesson  83 

5.  9  A.,  12  fields  of  9  A.  each.     6.  $  3598.14,  $  9445.28, 
$  238.95,  $  874.98.         7.   $  7659.18,  $  6648.75,  $  2190.96, 


260  ANSWERS 

$  9877.23.  9.  $25,  $  6 ;  $  96,  $  4 ;  88  mi.,  6  mi. ;  75 
of  the  unit,  1  of  the  unit ;  35  of  the  unit,  4  of  the  unit. 
10.  $  23,300.  11.  35  bu.  12.  8  da.  16.  $  45,  9  da. 
19.  $  13.50.  20.  $  155.25.  22.  $  240.  23.  $  3,  $  9. 


Lesson  84 
4.  Add  zero.        5.   Add  two  zeros.        12.   16  bu.  2  pk. 

Lesson  85 

10.     $1626.47,       $1134.19,       $793.44,       $1995.21. 

11.  $3999.97,       $5394.61,       $12,779.69,      $5439.09. 

12.  33,431  sq.  mi.          13.   391  sq.  mi.          14.   $308.96, 
$  180.40,  $  5700.48,  $  475.59.         15.   $  178.16,  $  4086.17, 
$  5579.91,  $  15,080.64.         16.    1250  sq.  mi.        17.   7300 
sq.  mi.       18.   $  5725,  $  11,450.       19.   $  277.68,  $  172.74, 
$  303.48,  $  124.75.     20.   $  537.44,  $  2553.32,  $  14,106.32, 
$  24,104.52.         21.   $  13,100.         22.   $  979.40,  $  708.05, 
$  376.12,  $  649.15.         23.   636  sheep.     The  quantity  and 
the  unit.     The  number.     24.   144. 

Lesson  86 

9.  912,  1392,  864,  2432,  $  1600,  $  752.  10.  1536  Ib. 
11.  507.  12.  $575.  13.  $980,  $221,  2176  Ib., 
1026  mi.,  304  mi.,  $  1152.  15.  1638,  5293,  8811,  5394, 
7050,  7396.  16.  5544,  5632,  2912,  7224,  23,360,  66,975. 
17.  $531.12,  $1162.89,  $464.64,  $2824.90,  $979.02, 
$  1386.49.  18.  $  1762.65,  $  6221.16,  $  7823.99,  $  1156.34, 
$  6533.15,  $  5095.24.  19.  $  5031.  20.  2592  mi. 


ANSWERS  261 

Lesson  87 

2.  43,  32, 62,  62,  $  64,  48.  3.  33,  56,  75,  72-4,  33,  $  56, 
$  75.  4.  $  31,  5.  37  hr.  6.  36  cows.  7.  $  23. 

11.  139,  135,  85,  154.          12.   44,  31;  48,  40;  731,  14; 
211;  580,  9;  77,  25;  281,  81;   86,  39.          13.   72   da., 
167  da.,  907  da.     14.  312  q.     15.  49  wk.,  $  14.     16.  $  96. 

Lesson  88 

2.  201,  13 ;  161,  47  ;  121,  6 ;  87,  46 ;  393,  18 ;  126,  18 ; 
55,  60;  78,  13;  71,  10;  113,  40;  529,  2;  1454,  27. 
3.  225  lb.,  $  12.25.  4.  36  bu.,  $  28.80.  5.  $  128. 
6.  $75,  15  A.,  $1125.  7.  $55,  $2340.  8.  4  doz. 

9.  757,  20 ;  1428,  35 ;  943,  21 ;  577,  36 ;  2073,  5 ;  871, 11 ; 
1581,  10 ;  790,  33 ;  707,  14 ;  3840,  7 ;  2313,  39 ;  5655,  2. 

10.  545  rugs.         11.   $  7.41,  $  7.50,  $  2.94,  $  .33,  $  .22, 
$.06,  $.14,  $.04.          12.   $1.23,  $2.94,   $1.94,  $.54, 
$1.34,    $.75,    $29.74,    $5.52,    $8.63.    '        13.   $4.85. 
14.   $3.15. 

Lesson  89 

8.  8  lb.  9.  4.  10.  3.  11.  2.  12.  12.  13.  250. 
14.  52, 14, 15,  27,  36,  25.  15.  72,  6  doz.  16.  16.  17.  17. 
18.  326,  $13.04.  19.  250  bu.,  23^.  20.  150  bu. 

Lesson  90 

4.  $63.98.  5.  $39.71.  6.  $20.59.  7.  15^  per 
100  lb.  8.  $1503.25.  9.  $56.26.  10.63^.  11.  $4.63. 

12.  $5.45.       13.   33^.       14.   226.       15.   324.       16.   125. 


262  ANSWERS 

Lesson  93 

1.  20,714,  2071.4,  207.14,  20.714.       2.   132.23,  90.638, 
1603.584.    a  15.046,  1.905  bu.    5.  67.616  A.    6.  19.26  mi. 
7.  2.114,  4.386,  12.631,  17.629.       8.  2.216,  5.244,  1.740, 
160.739.         9.  4.125yd.         10.   67.125  A.         11.   .875. 
13.  10.56  A.,  1.712  da.     14.  10.56  A.,  1.712  da.     15.  .840, 
5.94,  24.164,  65.872,  182.133.        16.  34.08,  102,  3135.6, 
28.248,   3.648.          17.   173.25,   54.918,   283.986,   1621.5. 
216.432.         18.   196.855.         20.   28.375.         21.   $33.75. 
22.  $2106.      23.  8.64;  8.64;  1.536;  1.536;  4.24;  $4.24; 
$61.44;     66.04;     66.04;     133.56;     133.56.  24.   60. 
25.  33.264  yd.,  2.736  yd. 

Lesson  94 

2.  2.163,  2.944,  9.412,  .299,  19.695,  3.313,  2.498,  .792, 
.351,  .068,  2.248,  .917,  .999,  8.646,  10.853.      3.  16.172  mi. 
4.   $  .875.       5.   67.2  cu.  in.      6.   57.75  cu.  in.       8.   1.307, 
3.12,  .142,  .409,  4.17,  1.411,   48.7,  1.66.         9.   $32.25. 
10.   $.875;    $9.375.         12.   11.5,   8.77,   361.5,   .725,   60, 
.049,  9.5,  11.15,  .203,  25,  4.5,  42,  8.41,  5.24,  1200,  52, 
12.52,  .387,  5.63,  12.        13.   29.       14.   600.       15.   90^; 
$  1.17.      18.   6.6,  126,  287, '67.7,  68,  2.1,  25.96+,  81,  6.24, 
35.08,  .875,  123.6,  20,  200,  12,  40,  600,  400.       20.   .875. 
21.  23.      22.  320.      23.  .33 ;  .67.      24.  300.      25.  60  da. 

Lesson  95 

23.  $32.      24.  $25.      25.  $100.      27.30^.      29.  $12, 
$15.       30.   36  yr.       31.   $60,  $720. 


ANSWERS  263 

Lesson  96 


9.  50  f.       10.  2100.       11.   $3000,  $7500.      12. 
20^.        13.   $45.        14.   $35.        15.   1500.       18.   331%. 

19.  25%.     20.  33|-%.     21.  75^.     22.  $3200.     23.  2700. 
24.   $4800. 

Lesson  97 

5.  20%,  60%.      6.  75%.      7.  24.      8.   80%.      9.  20%, 
60^.     10.  25%.     11.  $3.     12.  5£      13.  27^.      14.  $48. 
15.  $5.      16.  25%.      17.  33|%.      18.  $18.      19.   50%. 

20.  $40.      21.   $1000.       22.'  300.       23.   58J%. 

Lesson  98 

6.  $220.      7.  2  mi.      8.  $  84.      9.  $3000.      23.12%%. 
24.    10%.        25.    50%. 

Lesson  99 

5.  14.  6.  60%,  $36.  7.  6T.  8.  $27.  9.  $56. 
10.60%.  11.  25%,  331%.  12.  25%,  33$%.  13.  640  bu. 
14.  3hr.  15.  $3.60.  16.  $375.  17.  33^%,  20%,  40%, 
16f%,66f%.  18. 25%,16|%,33i%.  19.20%.  20.20%. 

Lesson  100 

1.  1,  2,  3,  4,  and  6  in. ;  2.  2.  4  ;  4.  3.  24  apples  ; 
30  £  4.  36  in.  5.  14  times  the  unit.  6.  54  apples. 
7.  30  mi.  8.  45  times.  9.  $  20,500.  10.  139  bu. ; 
$139.  11.  $14.  12.  $20;  $40;  $80.  13.  $4;  2. 
14.  12.75  T.  15.  972  sq.  ft.  16.  24  mi.  17.  120  mi. 
18.  $  175.  19.  195  Ib.  20.  $  115.05 ;  $  34.95. 


264  ANSWERS 

Lesson  101 

1.  9  times,  4  in.  2.  9,  £.  3.  $6,  $18;  A's  share. 
4.  A  $15,  B  $10,  C  $5;  C's  share.  3.  $3;  8  yd.;  $3, 
i.e.  the  selling  price  of  1  yd.  of  each.  10.  30  sq.  in. 
11.  4.  12.  i;  45  mi.  13.  1,25%.  14.  9  sq.ft. 
15.  $  36 ;  $  12 ;  $  4.  16.  12.  17.  5  times ;  £  f t. ;  5. 
18.  3  times,  £  ft. ;  3.  19.  1  ft.,  2 ;  \  yd.,  3,  etc.  20.  $  f , 
4,  $  |,  $  f  21.  3  ft.  22.  \  wk.  or  4  da.  23.  5  times. 

Lesson  102 

1.  24.  2.  $  4800.  3.  30  da.  4.  $  1.  5.  $  8  each. 
6.  98  Ib.  7.  14  Ib.  a  Load  of  wheat ;  624  Ib.  9.  $  10.50 ; 
$5.49.  10.  $180.48.  11.  $57.60.  12.  $3600. 

13.  $3.75.       14.   10%.       15.   36  yr.       16.   16f%;  $150. 
17.  36  da.       18.  20%.       19.   $2250.       20.   18,24. 

Lesson  103 

1.  $129.34,  $176.66,  $186.91,  $185.77,  $155.21, 
$294.59;  $1128.48.  2.  $311.10,  $302.33,  $328.67, 
$292.72,  $303.60,  $370.98;  $1909.40.  3.  $455.38, 
$  446.91,  $  416.68,  $  404.40,  $  361.62,  $  488.82 ;  $  2573.81. 
4.  26,370 ;  25,687;  23,202 ;  34,739.  5.  100,777  ;  $  144,658; 
243,296.  6.  540,  580,  595,  622,  665,  662.  7.  37267.576 ; 
33393.256;  27383.872.  8.  $2471.17;  $5661.77; 

$1652.97.  9.   $2298.35;       $1670.92;       $193.93. 

10.   $1627.26;     $2995.81;     $1077.91.         11.   $473.10; 
$2365.45;      $1061.41.  12.   $801.55;       $6874.36; 

$3076.78.  13.   $518.22;       $3917.45;       $72.73. 

14.  $2521.33;  $890.40;  $1653.97.       15.   9683;  89,169; 
10,360.         16,   24,568;   47,568;    15,837,         17.   322,378; 


ANSWERS  265 

31,046;    331,566.  18.   138.276;    110.242;    120.636. 

19.   28.945;    18.742;    55.794.  20.   65.187;    20.792; 

29.952.        21.   121.573 ;  221.11 ;  535.248.        22.   369.351 ; 
20.728;     27.895.  23.   390.527;     26.998;     285.896. 

24.   146.169;   629.29;   66.469. 

Lesson  104 

1.  14,592;  10,975;  73,270;  45,968;  82,944. 
2.  $1561.28;  $2987.52;  $1477.48;  $1152.30; 
$3471.75.  3.  $741.78;  $1763.32;  $2543.30;  $5287.92; 
$2516.85.  4.  2,175,918;  1,341,555;  3,140,880; 
1,739,298;  1,380,624.  5.  150,843;  138,996;  98,304; 
78,625;  53,119.  6.  82,276;  50,745;  55,660;  244,800; 
294,000.  7.  325,613;  466,620;  209,348;  114,552; 
674,250.  8.  352,820;  680,748;  779,492;  2,506,980; 
3,281,200.  9.  2,887,794;  968,877;  3,653,376;  8,567,280; 
1,208,466.  10.  $20,646.72;  $4042.50;  $4715.92; 
$17,914;  $8625.77.  11.  $13,335.84;  $17,965.30; 
$11,689.05;  $13,391;  $13,210.08.  12.  $9716.31; 
$  2175.39  ;  $  4120.68  ;  $  21,282.57  ;  $  6557.04. 
13.  $29,403;  $9421.50;  $22,051.47;  $23,037.84; 
$34,159.42.  14.  15,963.75;  3707.172;  404.976; 
43.365;  110.25.  15.  2737.455;  108.206;  2352.96; 
1378.167;  294.35.  16.  94,479;  1571.832;  7467.9; 
179,101.8;  1462.926.  17.  155,  25;  52,  31;  110,  41; 
201,  25.  18.  72,  20 ;  85,  65 ;  38,  33 ;  311,  12.  19.  188, 
4 ;  62,  45 ;  124,  54 ;  65,  52.  20.  11,  192 ;  24,  232 ;  8, 
67 ;  10,  274.  21.  52,  79 ;  43,  71 ;  14,  99 ;  9,  388.  22.  49, 
195;  11,  139;  19,  238;  3,  472.  23.  196,  78;  30,  299; 
115,  98;  68,  487.  24.  46,  509;  61,  258;  469,  9;  114, 
97.  25.  21,  169;  24,  1C.2;  143,  456;  215,  210. 


Public  School  Arithmetic 

BASED    ON 
McLELLAN  AND   DEWEY'S 

"PSYCHOLOGY  OF   NUMBER" 

BY 

J.  A.  McLELLAN,  A.M.,  LL.D., 

AND 

A.  F.  AMES,  A.B. 


I2mo.    Strong  Buckram.    Price,  60  cents,  net. 


This  book,  based  upon  sound  psychological  principles,  stands  for  a 
needed  reform  in  the  methods  of  teaching  Arithmetic. 

SPECIAL    FEATURES. 

The  treatment  of  the  subject  is  in  strict  line  with  the  idea  of  num- 
ber as  measurement. 

This  true  idea  of  number  running  through  the  whole  work  estab- 
lishes the  unity  of  the  whole. 

Fractions  are  divested  of  their  traditional  difficulty  by  being  placed 
in  their  true  relation  to  integers. 

Great  care  has  been  taken  in  selecting  and  grading  the  examples. 

This  treatment  of  the  subject  will  prove  a  good  preparation  for 
algebra. 

THE    MACMTLLAN    COMPANY, 

66   FIFTH   AVENUE,   NEW   YORK. 


COMMENTS. 

"  I  can  see  that  it  is  an  important  contribution  to  the  art  of  teaching  numbers." 
—  W.  T.  HARRIS,  U.S.  Commissioner,  Bureau  of  Education. 

"  From  a  careful  examination  it  seems  to  me  to  have  many  advantages  over  the 
books  on  the  subject  now  in  use.  Its  wise  omission  of  topics  of  no  practical  use,  the 
clearness  of  its  methods  and  problems,  and  its  neat  typography  appeal  to  every 
teacher  who  has  occasion  to  deplore  the  bulky  and  involved  arithmetics  in  so  many 
of  our  schools."  — GEORGE  GILBERT,  Principal  Chester  Academy,  Chester,  Pa. 

"I  heartily  approve  of  the  method  of  this  book."  —  W.  B.  SMITH,  McDonogh 
School,  McDonogh,  Md. 

"  The  processes  are  explained  logically  and  the  subjects  are  arranged  in  their 
proper  order  in  the  course.  The  examples  given  are  such  as  require  thought  and  at 
the  same  time  are  not  such  as  can  be  considered  unfairly  puzzling,  nor  are  they  too 
simple,  but  are  all  such  as  might  be  learned  from  some  of  the  preceding  parts  of  the 
book."  —  FREDERICK  DOOLITTLE,  Acting  School  Visitor  and  Clerk  of  Committee 
on  Education,  of  Connecticut. 

"  This  volume  is  a  very  successful  attempt  to  give  expression  to  the  better  teach- 
ing of  psychology  as  to  the  growth  and  development  of  the  idea  of  number.  The 
plan  of  the  work  is  thoroughly  scientific,  the  methods  are  well  presented  and  the  ex- 
amples well  chosen.  This  little  book  should  assist  greatly  in  the  reform  in  teaching 
arithmetic,  now  in  progress." — PROF.  ALFRED  I.  DE  LURY,  University  of  Toronto. 

"  This  book  contains  many  admirable  features.  I  like  especially  the  early  intro- 
duction of  decimal  operations."  —  CYRUS  BOGER,  A.M.,  Superintendent  Schools, 
Lebanon,  Pa. 

"  Naturally  I  am  pleased  with  the  extent  to  which  the  bpok  bases  the  treatment 
of  fundamental  operations  of  fractions  and  ratio  upon  the  dea  of  measure  and  of 
numbers  as  units  of  measurement.  I  am  particularly  struck  with  the  fact  that  the 
pupil's  attention  is  definitely  called  to  some  special  quantity  or  whole  which  furnishes 
the  object  of  attention,  and  within  which,  so  to  speak,  the  numerical  processes  take 
place;  also  with  the  clearness  and  conciseness  of  the  method  of  treatment;  the  logi- 
cal order  of  the  selection  of  topics;  and  the  exclusion  of  useless  and  irrelevant  mat- 
ter. The  simplification  of  treatment  due  to  sticking  close  to  fundamental  principles, 
must  recommend  the  book  to  teachers  and  pupils  who  have  been  bewildered  by  the 
great  number  of  topics  treated  in  the  ordinary  aiithmetic  —  topics  which  do  not 
differ  at  all  in  their  logical  or  arithmetical  basis,  but  are  simply  different  practical 
expressions  of  the  same  principle.  I  wish  the  book  the  success  it  deserves."  —  PRO- 
FESSOR DEWEY,  University  of  Chicago. 

"  '  The  Psychology  of  Number,'  by  Professors  McLellan  and  Dewey,  placed  on  a 
rational  basis  the  methods  to  be  pursued  in  the  elementary  treatment  of  number. 
This  has  now  been  followed  by  '  The  Public  School  Arithmetic,'  by  Professors 
McLellan  and  A.  F.  Ames,  in  which  these  rational  methods,  set  forth  in  the  former 
work,  are  systematically  and  successfully  presented.  The  special  feature  of  this 
book  consists  in  its  treatment  of  number  as  the  result  of  measurement.  The  authors 
have  brought  out  very  clearly  the  proper  methods  of  dealing  with  the  fundamental 
operations,  with  fractions,  and  with  the  commercial  rules.  The  definitions  are  con- 
sistent and  accurate  — a  feature  not  common  in  elementary  texts  of  arithmetic. 
There  is  an  excellent  collection  of  well-graded  examples.  Few  of  the  tricky  prob- 
lems which  have  done  so  much  to  discredit  arithmetic  are  to  be  found.  The  book 
consequently  deserves  speedily  to  win  a  place  among  recognized  text-books."  — 
PROFESSOR  McKAY,  McMaster  University. 

"  One  of  those  wise  books  that  make  school  study  more  pleasant  and  effective 
than  in  the  old  days  when  routine  study  was  the  rule.  .  .  .  Both  teachers  and  pupils 
will  welcome  this  very  valuable  book."  —  Saturday  Evening  Gazette,  Boston. 


THE    MACMTLLAN    COMPANY, 

66  FIFTH   AVENUE,   NEW  YORK. 


FOURTEEN  DAY  USE 

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